ecosystemSize
Emanuele Giacomuzzo
2024-07-01 11:15
## [1] "!! high !! The experiment investigate the effects of two disturbance levels: low and high. To make it easier to interpet, we showcase only one of the two disturbance levels. In this document we showcase only the high disturbance)"Design
Ecosystem size is a key factor driving biodiversity and ecosystem function. Larger ecosystems contain more species and can be hubs of dispersal and resource flows in networks of multiple ecosystems. However, whether and how ecosystem size and resource flows interact to affect biodiversity and ecosystem function has been largely overlooked. Here, we investigated how ecosystem size asymmetry affects biodiversity and function of two-ecosystem meta-ecosystems connected through flows of non-living resources. We conducted microcosm experiments, mimicking resource flows between ecosystems of different sizes, yet otherwise being identical. We found that meta-ecosystems with asymmetric ecosystem sizes had higher β-diversity but lower α-diversity and ecosystem function (total biomass) than their unconnected counterparts, while such an effect was not found for meta-ecosystems of identical ecosystem sizes. Our work demonstrates of how cross-ecosystem dynamics modulated by differences in ecosystem sizes affect biodiversity and function, with a direct implication for conservation and management of connected ecosystems.
Parameters
Parameters for R markdown and the general running of the code.
start_time = Sys.time()
knitr::opts_chunk$set(message = FALSE,
cache = FALSE,
autodep = FALSE)
recompute_lengthy_analyses = FALSE Parameters related to resource flows.
disturbance_levels = c("low", "high")
n_disturbance_levels = length(disturbance_levels)
resource_flow_days = c(5, 9, 13, 17, 21, 25)
first_resource_flow = resource_flow_days[1]Parameters related to sampling.
total_frames = 125
volume_recorded_μl = 34.4
time_points = 0:7
time_points_without_t0 = 1:7
time_point_names = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")
sampling_days = c(0, 4, 8, 12, 16, 20, 24, 28)
first_time_point = 0
last_time_point = length(sampling_days) - 1
n_time_points = last_time_point + 1
nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2) #Videos taken for each time point for each culture. At t0 we took 12 videos of the large bottle from which we started the cultures. Write why 2 at the end.
videos_taken = data.frame(time_point = 0 : 7,
nr_videos = c(12, 1, 1, 1, 1, 1, 2, 2))
n_videos_taken_t0 = nr_videos[1]
time_point_day = data.frame(time_point = first_time_point:last_time_point,
day = sampling_days,
video_replicates = nr_videos)
videos_to_take_off = data.frame(culture_ID = NA,
time_point = NA,
file = NA) %>%
add_row(culture_ID = 137-110,
time_point = 7,
file = 137) %>%
slice(-1)
n_cultures = 110
total_number_of_video_rows = sum(nr_videos * n_cultures)Parameters related to protists.
protist_species = c("Ble", "Cep", "Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi", "Spi_te", "Tet")
protist_species_indiv_per_volume = paste0(protist_species, "_indiv_per_volume")
protist_species_indiv_per_ml = paste0(protist_species, "_indiv_per_ml")
protist_species_dominance = paste0(protist_species_indiv_per_ml, "_dominance")
protist_species_total = paste0(protist_species, "_tot_indiv")
n_protist_species = length(protist_species)
first_protist = protist_species[1]
last_protist = protist_species[n_protist_species]
species_IDD_with_13_threshold = c("Col", "Eug", "Eup", "Lox", "Pau", "Pca", "Spi_te", "Tet")
species_IDD_with_13_threshold_indiv_per_volume = paste0(species_IDD_with_13_threshold, "_indiv_per_volume")
species_IDD_with_40_threshold = c("Ble", "Cep", "Spi")
species_IDD_with_40_threshold_indiv_per_volume = paste0(species_IDD_with_40_threshold, "_indiv_per_volume")Parameters related to ecosystems.
ecosystems_to_take_off = 60 #Culture ID = 60 as it was spilled (small unconnected, high disturbance, system nr = 40)
ecosystems_info = read.csv(here("2_data", "ecosystems_info.csv"), header = TRUE)
columns_ecosystems = c("time_point",
"day",
"culture_ID",
"system_nr",
"disturbance",
"ecosystem_type",
"ecosystem_size",
"ecosystem_size_ml",
"size_connected_ecosystem",
"metaecosystem",
"metaecosystem_type")
columns_treatments = columns_ecosystems[!columns_ecosystems %in% c("system_nr", "culture_ID")]
variables_ecosystems = c("bioarea_mm2_per_ml",
"bioarea_tot_mm2",
"indiv_per_ml",
"indiv_tot",
"species_richness",
"shannon",
"simpson",
"inv_simpson",
"evenness_pielou",
"median_body_area_µm2",
paste0(protist_species, "_indiv_per_ml"),
paste0(protist_species, "_tot_indiv"),
paste0(protist_species_indiv_per_ml, "_dominance"))
baseline_columns = paste0("baseline_", variables_ecosystems)
ecosystem_types_ordered = c("Small connected to large",
"Small connected to small",
"Small unconnected",
"Medium connected to medium",
"Medium unconnected",
"Large connected to small",
"Large connected to large",
"Large unconnected")
treatments_and_controls = data.frame(treatment = c("Small connected to small",
"Small connected to large",
"Medium connected to medium",
"Large connected to large",
"Large connected to small"),
control = c("Small unconnected",
"Small unconnected",
"Medium unconnected",
"Large unconnected",
"Large unconnected"))
n_treatments = length(unique(treatments_and_controls$treatment))
n_controls = length(unique(treatments_and_controls$control))
n_replicates = 5
n_ecosystem_types = 8Parameters related to size classes.
n_size_classes = 12
columns_classes = c(columns_ecosystems,
"size_class_n",
"mean_class_area_µm2")Parameters related to meta-ecosystems.
metaecosystems_to_take_off = ecosystems_info %>%
filter(culture_ID %in% ecosystems_to_take_off) %>%
pull(system_nr) %>%
unique
system_nr_metaecosystems = ecosystems_info %>%
filter(metaecosystem == "yes") %>%
pull(system_nr) %>%
unique
n_metaecosystems = length(system_nr_metaecosystems)
variables_metaecos = c(
"total_metaecosystem_bioarea_mm2",
"jaccard_index",
"bray_curtis",
"beta_spatial_turnover",
"beta_nestedness",
"beta_total",
"metaecosystem_richness")
metaecosystem_types_ordered = c(
"Small-Small meta-ecosystem",
"Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Large-Large meta-ecosystem",
"Small-Large meta-ecosystem",
"Small-Large unconnected")Name of the axes per response variable.
axis_names = data.frame(variable = NA,
axis_name= NA) %>%
add_row(variable = "day", axis_name = "Time (day)") %>%
add_row(variable = "ecosystem_size_ml", axis_name = "Patch size (ml)") %>%
add_row(variable = "log_size_class", axis_name = "Log size (μm2)") %>%
add_row(variable = "class_indiv_per_µl", axis_name = "Density (ind/ml)") %>%
add_row(variable = "bioarea_mm2_per_ml", axis_name = "Biomass (mm2/ml)") %>%
add_row(variable = "bioarea_mm2_per_ml_d", axis_name = "Bioamass ES") %>%
add_row(variable = "bioarea_tot", axis_name = "Total Biomass (mm2)") %>%
add_row(variable = "total_metaecosystem_bioarea_mm2", axis_name = "Total Biomass (mm2)") %>%
add_row(variable = "species_richness", axis_name = "Species Richness") %>%
add_row(variable = "species_richness_d", axis_name = "Species Richness ES") %>%
add_row(variable = "mean_richness", axis_name = "Mean α-Diversity (Shannon)") %>%
add_row(variable = "mean_shannon", axis_name = "Mean α-Diversity (Shannon)") %>%
add_row(variable = "shannon", axis_name = "Biodiversity (Shannon)") %>%
add_row(variable = "shannon_d", axis_name = "Biodiversity ES (Shannon ES)") %>%
add_row(variable = "bray_curtis", axis_name = "β-Diversity (Bray-Curtis)") %>%
add_row(variable = "beta_spatial_turnover", axis_name = "Turn over (Simpson pair-wise dissimilarity)") %>%
add_row(variable = "beta_nestedness", axis_name = "Nestedness (nestedness-fraction of Sorensen)") %>%
add_row(variable = "beta_total", axis_name = "Tot β-Diversity (Sorensen)") %>%
add_row(variable = "metaecosystem_richness", axis_name = "γ-Diversity (Species Richness)") %>%
add_row(variable = "indiv_per_ml", axis_name = "Abundance (ind/ml)") %>%
add_row(variable = "indiv_per_ml_d", axis_name = "Abundance ES") %>%
add_row(variable = "median_body_area_µm2", axis_name = "Median Body Size (µm²)") %>%
add_row(variable = "median_body_area_µm2_d", axis_name = "Median Body Size ES") %>%
add_row(variable = "Ble_indiv_per_ml", axis_name = "Ble Density (ind/ml)") %>%
add_row(variable = "Cep_indiv_per_ml", axis_name = "Cep Density (ind/ml)") %>%
add_row(variable = "Col_indiv_per_ml", axis_name = "Col Density (ind/ml)") %>%
add_row(variable = "Eug_indiv_per_ml", axis_name = "Eug Density (ind/ml)") %>%
add_row(variable = "Eup_indiv_per_ml", axis_name = "Eup Density (ind/ml)") %>%
add_row(variable = "Lox_indiv_per_ml", axis_name = "Lox Density (ind/ml)") %>%
add_row(variable = "Pau_indiv_per_ml", axis_name = "Pau Density (ind/ml)") %>%
add_row(variable = "Pca_indiv_per_ml", axis_name = "Pca Density (ind/ml)") %>%
add_row(variable = "Spi_indiv_per_ml", axis_name = "Spi Density (ind/ml)") %>%
add_row(variable = "Spi_te_indiv_per_ml", axis_name = "Spi te Density (ind/ml)") %>%
add_row(variable = "Tet_indiv_per_ml", axis_name = "Tet Density (ind/ml)") %>%
add_row(variable = "auto_hetero_ratio", axis_name = "Photosynthetisers-Heterotrops Ratio") %>%
add_row(variable = "Ble_indiv_per_ml_d", axis_name = "Ble Density ES") %>%
add_row(variable = "Cep_indiv_per_ml_d", axis_name = "Cep Density ES") %>%
add_row(variable = "Col_indiv_per_ml_d", axis_name = "Col Density ES") %>%
add_row(variable = "Eug_indiv_per_ml_d", axis_name = "Eug Density ES") %>%
add_row(variable = "Eup_indiv_per_ml_d", axis_name = "Eup Density ES") %>%
add_row(variable = "Lox_indiv_per_ml_d", axis_name = "Lox Density ES") %>%
add_row(variable = "Pau_indiv_per_ml_d", axis_name = "Pau Density ES") %>%
add_row(variable = "Pca_indiv_per_ml_d", axis_name = "Pca Density ES") %>%
add_row(variable = "Spi_indiv_per_ml_d", axis_name = "Spi Density ES") %>%
add_row(variable = "Spi_te_indiv_per_ml_d", axis_name = "Spi te Density ES") %>%
add_row(variable = "Tet_indiv_per_ml_d", axis_name = "Tet Density ES") %>%
add_row(variable = "Ble_indiv_per_ml_dominance", axis_name = "Ble Dominance (%)") %>%
add_row(variable = "Cep_indiv_per_ml_dominance", axis_name = "Cep Dominance (%)") %>%
add_row(variable = "Col_indiv_per_ml_dominance", axis_name = "Col Dominance (%)") %>%
add_row(variable = "Eug_indiv_per_ml_dominance", axis_name = "Eug Dominance (%)") %>%
add_row(variable = "Eup_indiv_per_ml_dominance", axis_name = "Eup Dominance (%)") %>%
add_row(variable = "Lox_indiv_per_ml_dominance", axis_name = "Lox Dominance (%)") %>%
add_row(variable = "Pau_indiv_per_ml_dominance", axis_name = "Pau Dominance (%)") %>%
add_row(variable = "Pca_indiv_per_ml_dominance", axis_name = "Pca Dominance (%)") %>%
add_row(variable = "Spi_indiv_per_ml_dominance", axis_name = "Spi Dominance (%)") %>%
add_row(variable = "Spi_te_indiv_per_ml_dominance", axis_name = "Spi te Dominance (%)") %>%
add_row(variable = "Tet_indiv_per_ml_dominance", axis_name = "Tet Dominance (%)") %>%
add_row(variable = "Ble_indiv_per_ml_dominance_d", axis_name = "Ble Dominance ES") %>%
add_row(variable = "Cep_indiv_per_ml_dominance_d", axis_name = "Cep Dominance ES") %>%
add_row(variable = "Col_indiv_per_ml_dominance_d", axis_name = "Col Dominance ES") %>%
add_row(variable = "Eug_indiv_per_ml_dominance_d", axis_name = "Eug Dominance ES") %>%
add_row(variable = "Eup_indiv_per_ml_dominance_d", axis_name = "Eup Dominance ES") %>%
add_row(variable = "Lox_indiv_per_ml_dominance_d", axis_name = "Lox Dominance ES") %>%
add_row(variable = "Pau_indiv_per_ml_dominance_d", axis_name = "Pau Dominance ES") %>%
add_row(variable = "Pca_indiv_per_ml_dominance_d", axis_name = "Pca Dominance ES") %>%
add_row(variable = "Sp_indiv_per_mli_dominance_d", axis_name = "Spi Dominance ES") %>%
add_row(variable = "Spi_te_indiv_per_ml_dominance_d", axis_name = "Spi te Dominance ES") %>%
add_row(variable = "Tet_indiv_per_ml_dominance_d", axis_name = "Tet Dominance ES") %>%
add_row(variable = "dominance", axis_name = "Dominance (%)") %>%
add_row(variable = "log_abundance", axis_name = "Log Abundance + 1 (ind/mm²)") %>%
add_row(variable = "abundance_hedges_d", axis_name = "Density ES") %>%
add_row(variable = "beta_diversity_from_unconnected", axis_name = "Divergence from unconnected") %>%
add_row(variable = "beta_diversity_from_previous_time", axis_name = "Temporal Divergence") %>%
add_row(variable = "beta_diversity_from_previous_time_d", axis_name = "Temporal Divergence ES") %>%
add_row(variable = "evenness_pielou", axis_name = "Evenness") %>%
add_row(variable = "evenness_pielou_d", axis_name = "Evenness ES") %>%
slice(-1)Colour and line type per ecosystem/meta-ecosystem type.
parameters_treatments = data.frame(treatment = NA,
colour = NA,
linetype = NA) %>%
add_row(treatment = "Small connected to large", colour = "#feb24c", linetype = "solid") %>%
add_row(treatment = "Small connected to small", colour = "#feb24c", linetype = "dashed") %>%
add_row(treatment = "Small unconnected", colour = "#bdbdbd", linetype = "solid") %>%
add_row(treatment = "Large connected to small", colour = "#3182bd", linetype = "solid") %>%
add_row(treatment = "Large connected to large", colour = "#3182bd", linetype = "dashed") %>%
add_row(treatment = "Large unconnected", colour = "#000000", linetype = "solid") %>%
add_row(treatment = "Medium connected to medium", colour = "#de2d26", linetype = "solid") %>%
add_row(treatment = "Medium unconnected", colour = "#737373", linetype = "solid") %>%
add_row(treatment = "Small-Large meta-ecosystem", colour = "#762a83", linetype = "solid") %>%
add_row(treatment = "Small-Large unconnected", colour = "#762a83", linetype = "dashed") %>%
add_row(treatment = "Medium-Medium meta-ecosystem", colour = "#1b7837", linetype = "solid") %>%
add_row(treatment = "Medium-Medium unconnected", colour = "#1b7837", linetype = "dashed") %>%
add_row(treatment = "Large-Large meta-ecosystem", colour = "#67000d", linetype = "solid") %>%
add_row(treatment = "Small-Small meta-ecosystem", colour = "#fc9272", linetype = "solid") %>%
slice(-1)Parameters for plotting.
figures_height_rmd_output = 7
legend_position = "top"
legend_width_cm = 2
size_legend = 12
size_x_axis = 13
size_y_axis = size_x_axis
boxplot_width = 2
dodging = 0.5
width_errorbar = 0.2
dodging_error_bar = 0.5
treatment_lines_linewidth = 1
treatment_points_size = 2.5
resource_flow_line_type = "solid"
resource_flow_line_colour = "#d9d9d9"
resource_flow_line_width = 0.3
zero_line_colour = "grey"
zero_line_line_type = "dotted"
zero_line_line_width = 0.5
zero_line_ES_line_type = "dotted"
zero_line_ES_colour = "grey"
zero_line_ES_line_width = 1
ggarrange_margin_top = 0
ggarrange_margin_bottom = 0
ggarrange_margin_left = 0
ggarrange_margin_right = 0
paper_width = 17.3
paper_height = 20
paper_units = "cm"
paper_res = 600
paper_y_axis_size = 9
paper_labels_size = 9
presentation_figure_size = 15
presentation_figure_width = 30
presentation_figure_height = 22
presentation_legend_size = 20
presentation_x_axis_size = 22
presentation_y_axis_size = presentation_x_axis_size
presentation_axes_size = 12
presentation_treatment_points_size = 5
presentation_treatment_linewidth = 2
presentation_figure_units = "cm"
presentation_figure_res = 600
grey_background_xmin = -Inf
grey_background_xmax = 7.5
grey_background_ymin = -Inf
grey_background_ymax = Inf
grey_background_fill = "#f0f0f0"
grey_background_alpha = 0.03
grey_background_color = "transparent"Parameters for modelling.
first_time_point_model = 2 #Time point 2 is the first after disturbance
last_time_point_model = last_time_point
optimizer_input = 'Nelder_Mead'
method_input = ''
compar_ex = "The full and fixed models are compared to the null model."
results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA) %>%
slice(-1)Data
Ecosystems information (ecosystems_info)
We start by importing the information about the 110 ecosystems of the experiment.
ecosystems_info = read.csv(here("2_data", "ecosystems_info.csv"), header = TRUE)Individuals (ds_individuals)
In this dataset (ds_individuals) each row represents an
individual at a time point.
# Import the individual data of t0. We considered cultures to be all the same at the beginning (t0). Because of this reason, we filmed only the bottles from which cultures were assembled. Because we want to plot also t0 for the different treatments, we want to assign the video of bottles to all cultures at t0.
ds_individuals_t0_not_elongated = read.csv(here("2_data",
"individuals_13_threshold",
"t0.csv")) %>%
mutate(time_point = as.numeric(str_extract(time_point, "\\d+")),
day = 0,
file = as.numeric(str_extract(file, "\\d+")),
video_replicate = file) %>%
select(time_point,
day,
video_replicate,
file,
id,
N_frames,
mean_area)
ds_individuals_t0_elongated = ds_individuals_t0_not_elongated %>%
map_dfr(.x = 1 : nrow(ecosystems_info),
.f = ~ ds_individuals_t0_not_elongated) %>%
arrange(id) %>% #Id refers to an individual
mutate(culture_ID = rep(1 : nrow(ecosystems_info),
times = nrow(ds_individuals_t0_not_elongated))) %>%
select(time_point,
day,
video_replicate,
file,
culture_ID,
id,
N_frames,
mean_area)
expect_equal(nrow(ds_individuals_t0_not_elongated) * nrow(ecosystems_info),
nrow(ds_individuals_t0_elongated))#Import t1-t4
ds_individuals_t1_to_t4 = NULL
for (time_point_i in time_points_without_t0) {
ds_individuals_t1_to_t4[[time_point_i]] = read.csv(here("2_data",
"individuals_13_threshold",
paste0("t",
time_point_i,
".csv"))) %>%
mutate(time_point = as.numeric(str_extract(time_point, "\\d+")),
day = time_point_day$day[time_point_day$time_point == time_point_i],
file = as.numeric(str_extract(file, "\\d+")),
video_replicate = ceiling(file/n_cultures)) #Until 110 video replicate = 1, then 2
}
ds_individuals_t1_to_t4 = ds_individuals_t1_to_t4 %>%
bind_rows() %>%
select(time_point,
day,
video_replicate,
file,
culture_ID,
id,
N_frames,
mean_area)# Bind t0 with t1-t4
ds_individuals = rbind(ds_individuals_t0_elongated,
ds_individuals_t1_to_t4) %>%
left_join(ecosystems_info,
by = "culture_ID") # Rename and select columns
ds_individuals = ds_individuals %>%
rename(ecosystem_size = patch_size,
ecosystem_size_volume = patch_size_volume) %>%
select(
disturbance,
disturbance_volume,
time_point,
day,
video_replicate,
culture_ID,
system_nr,
file,
eco_metaeco_type,
ecosystem_size,
ecosystem_size_volume,
metaecosystem,
metaecosystem_type,
mean_area,
N_frames
) %>%
rename(ecosystem_size_ml = ecosystem_size_volume,
ecosystem_type = eco_metaeco_type,
body_area_µm2 = mean_area)# Rename and reorder levels
ds_individuals <- ds_individuals %>%
mutate(ecosystem_type = case_when(ecosystem_type == "S" ~ "Small unconnected",
ecosystem_type == "M" ~ "Medium unconnected",
ecosystem_type == "L" ~ "Large unconnected",
ecosystem_type == "S (S_S)" ~ "Small connected to small",
ecosystem_type == "S (S_L)" ~ "Small connected to large",
ecosystem_type == "M (M_M)" ~ "Medium connected to medium",
ecosystem_type == "L (S_L)" ~ "Large connected to small",
ecosystem_type == "L (L_L)" ~ "Large connected to large",
TRUE ~ ecosystem_type),
ecosystem_type = factor(ecosystem_type,
levels = ecosystem_types_ordered))
ds_individuals <- ds_individuals %>%
mutate(ecosystem_size = case_when(ecosystem_size == "S" ~ "Small",
ecosystem_size == "M" ~ "Medium",
ecosystem_size == "L" ~ "Large",
TRUE ~ ecosystem_type),
ecosystem_size = factor(ecosystem_size,
levels = "Small",
"Medium",
"Large"))
ds_individuals <- ds_individuals %>%
mutate(size_connected_ecosystem = case_when(ecosystem_type == "Small connected to small" ~ "Small",
ecosystem_type == "Small connected to large" ~ "Large",
ecosystem_type == "Medium connected to medium" ~ "Medium",
ecosystem_type == "Large connected to large" ~ "Large",
ecosystem_type == "Large connected to small" ~ "Small",
TRUE ~ NA_character_))# Take off problematic videos
ds_individuals_before_taking_off_videos = ds_individuals
ds_individuals = ds_individuals %>%
filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))
diff = setdiff(ds_individuals_before_taking_off_videos, ds_individuals)
expect_equal(nrow(videos_to_take_off),
nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))# Take off problematic cultures
ds_individuals_before_taking_off_cultures = ds_individuals
ds_individuals = ds_individuals %>%
filter(!culture_ID %in% ecosystems_to_take_off)
expect_equal(setdiff(ds_individuals_before_taking_off_cultures,
ds_individuals) %>%
pull(culture_ID) %>%
unique(),
ecosystems_to_take_off)Patches (ds_ecosystems)
In this dataset (ds_ecosystems) each row represents a
ecosystem at a time point. I use the data from the 40 threshold analysis
for Ble, Cep, Spi and the data from the 13 threshold analysis for all
the other protists (Col, Eup, Lox, Pau, Pca, Spi te, Tet).
# Import & bind t0 datasets.
ds_ecosystems_t0 = read.csv(here("2_data",
"ecosystems_13_threshold",
"t0.csv")) %>%
mutate(time_point = as.numeric(str_extract(time_point, "\\d+")),
day = 0,
video_replicate = file) %>%
select(time_point,
day,
video_replicate,
file,
bioarea_per_volume,
indiv_per_volume)
species_ID_13_threshold_t0 = read.csv(here("2_data",
"species_ID_13_threshold",
paste0("t0.csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_13_threshold_indiv_per_volume))
species_ID_40_threshold_t0 = read.csv(here("2_data",
"species_ID_40_threshold",
paste0("t0.csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_40_threshold_indiv_per_volume))
ds_ecosystems_t0 = ds_ecosystems_t0 %>%
left_join(species_ID_13_threshold_t0,
by = "file") %>%
left_join(species_ID_40_threshold_t0,
by = "file") %>%
mutate(file = as.numeric(str_extract(file, "\\d+")))# Elongate t0 dataset.
ds_ecosystems_t0_elongated <- list()
for (video_i in 1 : n_videos_taken_t0) {
single_video = ds_ecosystems_t0 %>%
filter(file == video_i)
ds_ecosystems_t0_elongated[[video_i]] = ecosystems_info %>%
mutate(
time_point = 0,
day = 0,
file = single_video$file,
video_replicate = single_video$video_replicate,
bioarea_per_volume = single_video$bioarea_per_volume,
indiv_per_volume = single_video$indiv_per_volume,
Ble_indiv_per_volume = single_video$Ble_indiv_per_volume,
Cep_indiv_per_volume = single_video$Cep_indiv_per_volume,
Col_indiv_per_volume = single_video$Col_indiv_per_volume,
Eug_indiv_per_volume = single_video$Eug_indiv_per_volume,
Eup_indiv_per_volume = single_video$Eup_indiv_per_volume,
Lox_indiv_per_volume = single_video$Lox_indiv_per_volume,
Pau_indiv_per_volume = single_video$Pau_indiv_per_volume,
Pca_indiv_per_volume = single_video$Pca_indiv_per_volume,
Spi_indiv_per_volume = single_video$Spi_indiv_per_volume,
Spi_te_indiv_per_volume = single_video$Spi_te_indiv_per_volume,
Tet_indiv_per_volume = single_video$Tet_indiv_per_volume)
}
ds_ecosystems_t0_elongated = ds_ecosystems_t0_elongated %>%
bind_rows()# Clean the columns of t0
ds_ecosystems_t0 = ds_ecosystems_t0_elongated %>%
select(
file,
time_point,
day,
culture_ID,
video_replicate,
bioarea_per_volume,
indiv_per_volume,
all_of(protist_species_indiv_per_volume))
expect_equal(nrow(ds_ecosystems_t0), sum(n_videos_taken_t0 * n_cultures))# Import and bind t1-t4
ds_ecosystems_t1_to_t4 = NULL
for (time_point_i in time_points_without_t0) {
species_ID_13_threshold = read.csv(here("2_data",
"species_ID_13_threshold",
paste0("t", time_point_i, ".csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_13_threshold_indiv_per_volume))
species_ID_40_threshold = read.csv(here("2_data",
"species_ID_40_threshold",
paste0("t", time_point_i, ".csv"))) %>%
rename(Ble_indiv_per_volume = Ble,
Cep_indiv_per_volume = Cep,
Col_indiv_per_volume = Col,
Eug_indiv_per_volume = Eug,
Eup_indiv_per_volume = Eup,
Lox_indiv_per_volume = Lox,
Pau_indiv_per_volume = Pau,
Pca_indiv_per_volume = Pca,
Spi_indiv_per_volume = Spi,
Spi_te_indiv_per_volume = Spi_te,
Tet_indiv_per_volume = Tet) %>%
select(file,
all_of(species_IDD_with_40_threshold_indiv_per_volume))
ds_ecosystems_t1_to_t4[[time_point_i]] = read.csv(here("2_data",
"ecosystems_13_threshold",
paste0("t", time_point_i, ".csv"))) %>%
arrange(file) %>%
mutate(video_replicate = rep(1 : time_point_day$video_replicates[time_point_i+1],
each = n_cultures),
day = time_point_day$day[time_point_day$time_point == time_point_i]) %>%
select(
file,
time_point,
day,
video_replicate,
file,
culture_ID,
bioarea_per_volume,
indiv_per_volume)
ds_ecosystems_t1_to_t4[[time_point_i]] = ds_ecosystems_t1_to_t4[[time_point_i]] %>%
left_join(species_ID_13_threshold,
by = "file") %>%
left_join(species_ID_40_threshold,
by = "file")
}
ds_ecosystems_t1_to_t4 = ds_ecosystems_t1_to_t4 %>%
bind_rows()# Bind t0 with t1-t4
ds_ecosystems = rbind(ds_ecosystems_t0,
ds_ecosystems_t1_to_t4) %>%
left_join(ecosystems_info,
by = "culture_ID")
expect_equal(nrow(ds_ecosystems),
sum(sum(time_point_day$video_replicates) * n_cultures))# Reorder and rename columns
ds_ecosystems = ds_ecosystems %>%
rename(ecosystem_size = patch_size,
ecosystem_size_ml = patch_size_volume) %>%
select(
file,
time_point,
day,
disturbance,
culture_ID,
system_nr,
eco_metaeco_type,
ecosystem_size,
ecosystem_size_ml,
metaecosystem,
metaecosystem_type,
video_replicate,
bioarea_per_volume,
indiv_per_volume,
all_of(protist_species_indiv_per_volume)
) %>%
rename(ecosystem_type = eco_metaeco_type,
bioarea_µm2_per_μL = bioarea_per_volume) %>%
rename_all( ~ gsub("volume", "μL", .))# Rename and reorder levels
ds_ecosystems <- ds_ecosystems %>%
mutate(
ecosystem_type = case_when(
ecosystem_type == "S" ~ "Small unconnected",
ecosystem_type == "M" ~ "Medium unconnected",
ecosystem_type == "L" ~ "Large unconnected",
ecosystem_type == "S (S_S)" ~ "Small connected to small",
ecosystem_type == "S (S_L)" ~ "Small connected to large",
ecosystem_type == "M (M_M)" ~ "Medium connected to medium",
ecosystem_type == "L (S_L)" ~ "Large connected to small",
ecosystem_type == "L (L_L)" ~ "Large connected to large",
TRUE ~ ecosystem_type
),
ecosystem_type = factor(x = ecosystem_type,
levels = ecosystem_types_ordered),
ecosystem_size = case_when(
ecosystem_size == "S" ~ "Small",
ecosystem_size == "M" ~ "Medium",
ecosystem_size == "L" ~ "Large",
TRUE ~ ecosystem_size
),
metaecosystem_type = case_when(
metaecosystem_type == "S_S" ~ "Small-Small meta-ecosystem",
metaecosystem_type == "M_M" ~ "Medium-Medium meta-ecosystem",
metaecosystem_type == "L_L" ~ "Large-Large meta-ecosystem",
metaecosystem_type == "S_L" ~ "Small-Large meta-ecosystem",
TRUE ~ metaecosystem_type
),
size_connected_ecosystem = case_when(
ecosystem_type == "Small connected to small" ~ "Small",
ecosystem_type == "Small connected to large" ~ "Large",
ecosystem_type == "Medium connected to medium" ~ "Medium",
ecosystem_type == "Large connected to large" ~ "Large",
ecosystem_type == "Large connected to small" ~ "Small",
TRUE ~ NA_character_
),
time_point = as.numeric(str_extract(time_point, "\\d+")),
file = as.numeric(str_extract(file, "\\d+")),
)# Change units of measurments to ml
ds_ecosystems = ds_ecosystems %>%
mutate(bioarea_µm2_per_ml = bioarea_µm2_per_μL * 10^3,
bioarea_mm2_per_ml = bioarea_µm2_per_ml * 10^(-6),
Ble_indiv_per_ml = Ble_indiv_per_μL * 10^3,
Cep_indiv_per_ml = Cep_indiv_per_μL * 10^3,
Col_indiv_per_ml = Col_indiv_per_μL * 10^3,
Eug_indiv_per_ml = Eug_indiv_per_μL * 10^3,
Eup_indiv_per_ml = Eup_indiv_per_μL * 10^3,
Lox_indiv_per_ml = Lox_indiv_per_μL * 10^3,
Pau_indiv_per_ml = Pau_indiv_per_μL * 10^3,
Pca_indiv_per_ml = Pca_indiv_per_μL * 10^3,
Spi_indiv_per_ml = Spi_indiv_per_μL * 10^3,
Spi_te_indiv_per_ml = Spi_te_indiv_per_μL * 10^3,
Tet_indiv_per_ml = Tet_indiv_per_μL * 10^3)# Take off problematic videos
ds_ecosystems_before_taking_off_videos = ds_ecosystems
ds_ecosystems = ds_ecosystems %>%
filter(!(time_point %in% videos_to_take_off$time_point & file %in% videos_to_take_off$file))
diff = setdiff(ds_ecosystems_before_taking_off_videos, ds_ecosystems)
expect_equal(nrow(videos_to_take_off),
nrow(expand.grid(diff$culture_ID, diff$time_point, diff$file) %>% unique()))# Take off problematic cultures
ds_ecosystems_before_taking_off_cultures = ds_ecosystems
ds_ecosystems = ds_ecosystems %>%
filter(!culture_ID %in% ecosystems_to_take_off)
expect_equal(setdiff(ds_ecosystems_before_taking_off_cultures,
ds_ecosystems) %>%
pull(culture_ID) %>%
unique(),
ecosystems_to_take_off)# Average videos
ds_ecosystems = ds_ecosystems %>%
group_by(across(all_of(columns_ecosystems))) %>%
summarise(across(contains("_per_ml"), mean),
across(contains("_tot"), mean)) %>%
ungroup()
expect_equal(nrow(ds_ecosystems),
(n_cultures - length(ecosystems_to_take_off)) * length(time_points))# Add connection and individuals
ds_ecosystems = ds_ecosystems %>%
mutate(indiv_per_ml = !!rlang::parse_expr(paste(protist_species_indiv_per_ml,
collapse = " + ")))
ds_ecosystems = ds_ecosystems %>%
mutate(connection = ifelse(str_detect(ecosystem_type, "unconnected"),
"unconnected",
"connected"),
connection = factor(x = connection,
levels = c("unconnected", "connected")))# Calculate total response variable for the whole ecosystem
ds_ecosystems = ds_ecosystems %>%
mutate(bioarea_tot_mm2 = bioarea_mm2_per_ml * ecosystem_size_ml,
indiv_tot = indiv_per_ml * ecosystem_size_ml,
Ble_tot_indiv = Ble_indiv_per_ml * ecosystem_size_ml,
Cep_tot_indiv = Cep_indiv_per_ml * ecosystem_size_ml,
Col_tot_indiv = Col_indiv_per_ml * ecosystem_size_ml,
Eug_tot_indiv = Eug_indiv_per_ml * ecosystem_size_ml,
Eup_tot_indiv = Eup_indiv_per_ml * ecosystem_size_ml,
Lox_tot_indiv = Lox_indiv_per_ml * ecosystem_size_ml,
Pau_tot_indiv = Pau_indiv_per_ml * ecosystem_size_ml,
Pca_tot_indiv = Pca_indiv_per_ml * ecosystem_size_ml,
Spi_tot_indiv = Spi_indiv_per_ml * ecosystem_size_ml,
Spi_te_tot_indiv = Spi_te_indiv_per_ml * ecosystem_size_ml,
Tet_tot_indiv = Tet_indiv_per_ml * ecosystem_size_ml)# Calculate species dominance
ds_ecosystems = ds_ecosystems %>%
mutate(across(.cols = all_of(protist_species_indiv_per_ml),
.fns = list(dominance = ~ (. / indiv_per_ml) * 100),
.names = "{col}_dominance"))
expect_equal(unique(ds_ecosystems$Ble_indiv_per_ml_dominance[ds_ecosystems$indiv_per_ml == 0]), NaN)
if (FALSE %in% unique((ds_ecosystems$Ble_indiv_per_ml/ds_ecosystems$indiv_per_ml) *100 == ds_ecosystems$Ble_indiv_per_ml_dominance)) stop()# Calculate alpha diversity (Shannon, Simpson, Inverse Simpson, Evenness)
n_rows_ds_ecosystems_before_calculating_alpha = nrow(ds_ecosystems)
ds_ecosystems = calculate.alpha.diversity()
expect_equal(max(ds_ecosystems$species_richness),
length(protist_species))
expect_equal(nrow(ds_ecosystems),
n_rows_ds_ecosystems_before_calculating_alpha)# Calculate median body size
n_rows_ds_ecosystems_before_median_size = nrow(ds_ecosystems)
ds_median_body_size = ds_individuals %>%
group_by(time_point,
culture_ID,
file) %>%
summarise(median_body_area_µm2 = median(body_area_µm2)) %>%
group_by(time_point,
culture_ID) %>%
summarise(median_body_area_µm2 = mean(median_body_area_µm2))
expect_true(nrow(ds_median_body_size) <= nrow(ds_ecosystems)) #Ds median body size could be less because some cultures might be crashed and not have any individual.
ds_ecosystems_before_full_join = ds_ecosystems
ds_ecosystems = full_join(ds_ecosystems, ds_median_body_size)
expect_equal(nrow(ds_ecosystems),
n_rows_ds_ecosystems_before_median_size)# Calculate auto/heterotrophic ratio
ds_ecosystems = ds_ecosystems %>%
mutate(auto_hetero_ratio = (Eug_indiv_per_ml + Eup_indiv_per_ml) /
(Ble_indiv_per_ml +
Cep_indiv_per_ml +
Col_indiv_per_ml +
Lox_indiv_per_ml +
Pau_indiv_per_ml +
Pca_indiv_per_ml +
Spi_indiv_per_ml +
Spi_te_indiv_per_ml +
Tet_indiv_per_ml))Patch effect sizes (ds_ecosystems_effect_size)
In this dataset (ds_ecosystems_effect_size) each row
represents a treatment at a time point. It contains the effect size of
the connection of a ecosystem (connected vs unconnected).
# Calculate the mean & sd of response variables for each treatment/control at each time point
ds_ecosystems_effect_size = NULL
variable_nr = 0
for (variable_i in variables_ecosystems) {
variable_nr = variable_nr + 1
ds_ecosystems_effect_size[[variable_nr]] = ds_ecosystems %>%
filter(time_point >= 1,
!is.na(!!sym(variable_i))) %>%
group_by(across(all_of(columns_ecosystems[columns_ecosystems != "culture_ID" &
columns_ecosystems != "system_nr"]))) %>%
summarise(across(all_of(variable_i),
list(mean = mean,
sd = sd)),
sample_size = n()) %>%
rename_with( ~ paste0(variable_i, "_sample_size"),
matches("sample_size"))
}
ds_ecosystems_effect_size <- reduce(ds_ecosystems_effect_size,
full_join,
by = columns_ecosystems[columns_ecosystems != "culture_ID" &
columns_ecosystems != "system_nr"])
expect_equal(nrow(ds_ecosystems_effect_size),
n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)# Calculate the effect size (Hedge's d) for each treatment at each time point
for (variable_i in variables_ecosystems) {
ds_ecosystems_effect_size <- ds_ecosystems_effect_size %>%
mutate(
!!paste0(variable_i, "_d") := NA,
!!paste0(variable_i, "_d_upper") := NA,
!!paste0(variable_i, "_d_lower") := NA
)
}
row_n = 0
for (treatment_input in treatments_and_controls$treatment) {
for (time_point_input in time_points) {
row_n = row_n + 1
control_input = treatments_and_controls$control[
treatments_and_controls$treatment == treatment_input
]
treatment_row = ds_ecosystems_effect_size %>%
filter(ecosystem_type == treatment_input,
time_point == time_point_input)
control_row = ds_ecosystems_effect_size %>%
filter(ecosystem_type == control_input,
time_point == time_point_input)
for (response_variable in variables_ecosystems) {
hedges_d = calculate.hedges_d(
treatment_row[[paste0(response_variable, "_mean")]],
treatment_row[[paste0(response_variable, "_sd")]],
treatment_row[[paste0(response_variable, "_sample_size")]],
control_row[[paste0(response_variable, "_mean")]],
control_row[[paste0(response_variable, "_sd")]],
control_row[[paste0(response_variable, "_sample_size")]]
)
ds_ecosystems_effect_size[[paste0(response_variable, "_d")]][
ds_ecosystems_effect_size$ecosystem_type == treatment_input &
ds_ecosystems_effect_size$time_point == time_point_input] =
hedges_d$d
ds_ecosystems_effect_size[[paste0(response_variable, "_d_upper")]][
ds_ecosystems_effect_size$ecosystem_type == treatment_input &
ds_ecosystems_effect_size$time_point == time_point_input] =
hedges_d$upper_CI
ds_ecosystems_effect_size[[paste0(response_variable, "_d_lower")]][
ds_ecosystems_effect_size$ecosystem_type == treatment_input &
ds_ecosystems_effect_size$time_point == time_point_input] =
hedges_d$lower_CI
}
}
}
expect_equal(nrow(ds_ecosystems_effect_size),
n_ecosystem_types * (n_time_points-1) * n_disturbance_levels)Meta-ecosystems (ds_metaecosystems)
In this dataset (ds_metaecosystems) each row represents
a meta-ecosystem or a two-ecosystem unconnected system at a time
point.
#Find combinations of ecosystems in unconnected two-ecosystem systems.
ID_unconnected_S_low = ds_ecosystems %>%
filter(ecosystem_type == "Small unconnected",
disturbance == "low") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_M_low = ds_ecosystems %>%
filter(ecosystem_type == "Medium unconnected",
disturbance == "low") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_L_low = ds_ecosystems %>%
filter(ecosystem_type == "Large unconnected",
disturbance == "low") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_S_high = ds_ecosystems %>%
filter(ecosystem_type == "Small unconnected",
disturbance == "high") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_M_high = ds_ecosystems %>%
filter(ecosystem_type == "Medium unconnected",
disturbance == "high") %>%
pull(culture_ID) %>%
unique()
ID_unconnected_L_high = ds_ecosystems %>%
filter(ecosystem_type == "Large unconnected",
disturbance == "high") %>%
pull(culture_ID) %>%
unique()# Find combinations of ecosystems to create different two-ecosystem unconnected systems
combinations_S_and_L_low = crossing(ID_unconnected_S_low,
ID_unconnected_L_low) %>%
mutate(disturbance = "low",
metaecosystem_type = "Small-Large unconnected") %>%
rename(ID_first_ecosystem = ID_unconnected_S_low,
ID_second_ecosystem = ID_unconnected_L_low) %>%
select(disturbance,
metaecosystem_type,
ID_first_ecosystem,
ID_second_ecosystem)
combinations_S_and_L_high = crossing(ID_unconnected_S_high,
ID_unconnected_L_high) %>%
mutate(disturbance = "high",
metaecosystem_type = "Small-Large unconnected") %>%
rename(ID_first_ecosystem = ID_unconnected_S_high,
ID_second_ecosystem = ID_unconnected_L_high) %>%
select(disturbance,
metaecosystem_type,
ID_first_ecosystem,
ID_second_ecosystem)
combinations_M_and_M_low = combinat::combn(ID_unconnected_M_low,
m = 2) %>%
t() %>%
as.data.frame() %>%
rename(ID_first_ecosystem = V1,
ID_second_ecosystem = V2) %>%
mutate(disturbance = "low",
metaecosystem_type = "Medium-Medium unconnected") %>%
select(disturbance,
metaecosystem_type,
ID_first_ecosystem,
ID_second_ecosystem)
combinations_M_and_M_high = combinat::combn(ID_unconnected_M_high,
m = 2) %>%
t() %>%
as.data.frame() %>%
rename(ID_first_ecosystem = V1,
ID_second_ecosystem = V2) %>%
mutate(disturbance = "high",
metaecosystem_type = "Medium-Medium unconnected") %>%
select(disturbance,
metaecosystem_type,
ID_first_ecosystem,
ID_second_ecosystem)# Bind combinations
combinations_unconnected_systems = rbind(combinations_S_and_L_low,
combinations_S_and_L_high,
combinations_M_and_M_low,
combinations_M_and_M_high) %>%
mutate(system_nr = 1001:(1000 + nrow(.))) %>%
select(system_nr,
disturbance,
metaecosystem_type,
ID_first_ecosystem,
ID_second_ecosystem)# Find combinations of ecosystems that were connected to form meta-ecosystems.
combinations_metaecos = ds_ecosystems %>%
filter(time_point == 0,
metaecosystem == "yes") %>%
select(system_nr,
disturbance,
metaecosystem_type,
culture_ID) %>%
group_by(system_nr,
disturbance,
metaecosystem_type) %>%
summarise(ID_first_ecosystem = (mean(culture_ID) - 0.5),
ID_second_ecosystem = (mean(culture_ID) + 0.5)) %>%
as.data.frame()#Bind unconnected two-ecosystem systems and meta-ecosystems
ecosystem_combinations = rbind(combinations_unconnected_systems,
combinations_metaecos) %>%
mutate(connection = ifelse(metaecosystem_type %in% c("Medium-Medium unconnected",
"Small-Large unconnected"),
yes = "unconnected",
no = "connected"),
ecosystems_combined = paste0(ID_first_ecosystem, "|", ID_second_ecosystem))
n_ecosystems_combinations = nrow(ecosystem_combinations)#Create sets for SL unconnected, where in each set a small and a large ecosystems are paired differently. To do so, I keep the small ecosystems on the same order and perform permutations on large ecosystems.
SL_unconnected_sys_sets <- vector("list",
length(disturbance_levels))
for (disturbance_i in 1:length(disturbance_levels)) {
ID_small_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_levels[disturbance_i],
ecosystem_type == "Small unconnected") %>%
pull(culture_ID) %>%
unique()
ID_large_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_levels[disturbance_i],
ecosystem_type == "Large unconnected") %>%
pull(culture_ID) %>%
unique()
#Force small and large ecosystems vectors to have the same length
length_difference <- length(ID_small_ecosystems) - length(ID_large_ecosystems)
if (length_difference > 0) {
ID_large_ecosystems = c(ID_large_ecosystems,
rep("Patch taken off",
times = abs(length(ID_small_ecosystems) -
length(ID_large_ecosystems))))
} else if (length_difference < 0) {
ID_small_ecosystems = c(ID_small_ecosystems,
rep("Patch taken off",
times = abs(length(ID_large_ecosystems) -
length(ID_small_ecosystems))))
}
# Create dataframe
permutations_large = permn(ID_large_ecosystems)
SL_unconnected_sys_sets[[disturbance_i]] = data.frame(
disturbance = disturbance_levels[disturbance_i],
metaecosystem_type = "Small-Large unconnected",
connection = "unconnected",
ID_first_ecosystem = rep(ID_small_ecosystems, times = length(permutations_large)),
ID_second_ecosystem = unlist(permutations_large),
set = rep(1 : length(permutations_large), each = length(ID_small_ecosystems)))
expect_equal(nrow(SL_unconnected_sys_sets[[disturbance_i]]),
length(ID_small_ecosystems) * length(permutations_large))
SL_unconnected_sys_sets[[disturbance_i]] = SL_unconnected_sys_sets[[disturbance_i]] %>%
filter(!ID_first_ecosystem == "Patch taken off",
!ID_second_ecosystem == "Patch taken off") %>%
mutate(ID_first_ecosystem = as.double(ID_first_ecosystem),
ID_second_ecosystem = as.double(ID_second_ecosystem)) %>%
full_join(ecosystem_combinations %>%
filter(disturbance == disturbance_levels[disturbance_i],
metaecosystem_type == "Small-Large unconnected")) #Add system_nr & ecosystems_combined
}
SL_unconnected_sys_sets_before_binding = SL_unconnected_sys_sets
SL_unconnected_sys_sets = SL_unconnected_sys_sets %>%
bind_rows()expect_equal(nrow(SL_unconnected_sys_sets),
nrow(SL_unconnected_sys_sets_before_binding[[1]]) + nrow(SL_unconnected_sys_sets_before_binding[[2]]))
expect_equal(length(SL_unconnected_sys_sets %>%
pull(system_nr) %>%
unique()),
length(ecosystem_combinations %>%
filter(metaecosystem_type == "Small-Large unconnected") %>%
pull(system_nr) %>%
unique()))#WORK HERE
#Create sets for MM unconnected, where in each set two medium ecosystems small are paired differently. To do so, I ...
#Initialise MM_unconnected_sets. Assign 10^4 rows to each matrix so that we have enough rows not to run out of them when we try to assign values to them. Assign 4 columns which will include culture_ID of the first system, second culture_ID of the fist system, culture_ID of the second system, and second culture_ID of the second system.
MM_unconnected_sets = NULL
for(disturbance_i in 1:length(disturbance_levels)){
MM_unconnected_sets[[disturbance_i]] <- matrix(nrow = 10 ^ 4,
ncol = 4)
}
for (disturbance_i in 1:length(disturbance_levels)) {
ID_medium_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_levels[disturbance_i],
ecosystem_type == "Medium unconnected") %>%
pull(culture_ID) %>%
unique()
MM_unconnected_systems = combn(ID_medium_ecosystems,
2) %>%
t()
matrix_row = 0
for (first_system_i in 1:nrow(MM_unconnected_systems)) {
#Find culture IDs of the first system (what's the first system?)
first_system = MM_unconnected_systems[first_system_i, ]
for (second_system_i in 1:nrow(MM_unconnected_systems)) {
#Find culture IDs of the second system (what's the second system?)
second_system = MM_unconnected_systems[second_system_i, ]
shared_elements_among_systems = intersect(first_system,
second_system)
if (length(shared_elements_among_systems) == 0) {
matrix_row = matrix_row + 1
#Make first and second system into a set
MM_unconnected_sets[[disturbance_i]][matrix_row,] = c(first_system,
second_system)
print(MM_unconnected_sets[[disturbance_i]][matrix_row,])
}
}
}
#Tidy the dataset with all the ecosystem combinations
MM_unconnected_sets[[disturbance_i]] = MM_unconnected_sets[[disturbance_i]] %>%
as.data.frame() %>%
drop_na()
expect_equal(MM_unconnected_sets[[disturbance_i]] %>%
filter(V1 == V2 | V1 == V3 | V1 == V4 | V2 == V3 | V2 == V4 | V3 == V4) %>%
nrow(),
0)
#Reorder the dataset with all the ecosystem combinations
MM_unconnected_sets_reordered = data.frame(ID_first_ecosystem = NA,
ID_second_ecosystem = NA,
set = NA)
for (set_input in 1:nrow(MM_unconnected_sets[[disturbance_i]])) {
MM_unconnected_sets_reordered = MM_unconnected_sets_reordered %>%
add_row(
ID_first_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 1],
ID_second_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 2],
set = set_input
) %>%
add_row(
ID_first_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 3],
ID_second_ecosystem = MM_unconnected_sets[[disturbance_i]][set_input, 4],
set = set_input
)
}
#Add to a list
MM_unconnected_sets[[disturbance_i]] = MM_unconnected_sets_reordered %>%
drop_na() %>%
mutate(
disturbance = disturbance_levels[disturbance_i],
metaecosystem_type = "Medium-Medium unconnected",
connection = "unconnected"
)
#Add system nr
ID_combinations_MM_unconnected = ecosystem_combinations %>%
filter(disturbance == disturbance_levels[disturbance_i],
metaecosystem_type == "Medium-Medium unconnected")
MM_unconnected_sets[[disturbance_i]] = full_join(MM_unconnected_sets[[disturbance_i]],
ID_combinations_MM_unconnected)
}## [1] 6 7 8 9
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## [1] 64 65 62 63#Bind all sets of MM unconnected
MM_unconnected_sets = MM_unconnected_sets %>%
bind_rows()expect_equal(length(MM_unconnected_sets %>%
pull(system_nr) %>%
unique()),
length(ecosystem_combinations %>%
filter(metaecosystem_type == "Medium-Medium unconnected") %>%
pull(system_nr) %>%
unique()))#Bind SL and MM unconnected systems
unconnected_combinations_sets = rbind(SL_unconnected_sys_sets,
MM_unconnected_sets) %>%
select(disturbance,
metaecosystem_type,
connection,
set,
system_nr,
ID_first_ecosystem,
ID_second_ecosystem)Each row is a meta-ecosystem.
It contains also “fake” meta-ecosystems which I created from unconnected ecosystems (
metaecosystem type = Small-Large unconnected&metaecosystem type = Medium-Medium unconnected).Warning appear after the following code, as:
- alpha diversity is computed for a culture that is totally crashed, so it has not meaning.
- beta diversity is computed between a culture that is still alive and one that is totally crashed. Because one of the cultures is totally crashed, the Bray-Curtis index is 1.
#Compute meta-ecosystems for each time point
ds_metaecosystems = NULL
row_n = 0
for (combination in 1:n_ecosystems_combinations) {
for (time_point_input in time_points) {
row_n = row_n + 1
current_day = sampling_days[time_point_input + 1]
current_system_nr = ecosystem_combinations[combination, ]$system_nr
current_combination = ecosystem_combinations[combination, ]$ecosystems_combined
current_disturbance = ecosystem_combinations[combination, ]$disturbance
current_metaeco_type = ecosystem_combinations[combination, ]$metaecosystem_type
current_IDs = c(ecosystem_combinations[combination, ]$ID_first_ecosystem,
ecosystem_combinations[combination, ]$ID_second_ecosystem)
if (current_system_nr %in% metaecosystems_to_take_off)
next
if (current_IDs[1] == current_IDs[2])
next
species_vector_two_ecosystems = ds_ecosystems %>%
filter(time_point == time_point_input,
culture_ID %in% current_IDs) %>%
ungroup() %>%
select(all_of(protist_species_indiv_per_ml))
absence_presence_two_ecosystems <-
ifelse(species_vector_two_ecosystems > 0, 1, 0)
#Alpha diversity: Shannon (mean between the two ecosystems)
shannon_ecosystem_1 = diversity(species_vector_two_ecosystems[1, ], index = "shannon")
shannon_ecosystem_2 = diversity(species_vector_two_ecosystems[2, ], index = "shannon")
shannon_value = (shannon_ecosystem_1 + shannon_ecosystem_2) / 2
#Alpha diversity: Species richness (mean between the two ecosystems)
richness_ecosystem_1 = specnumber(species_vector_two_ecosystems[1, ])
richness_ecosystem_2 = specnumber(species_vector_two_ecosystems[2, ])
mean_richness_value = (richness_ecosystem_1 + richness_ecosystem_2) / 2
#Beta diversity: Jaccard
jaccard_index_value = vegdist(species_vector_two_ecosystems,
method = "jaccard") %>%
as.numeric()
#Beta diversity: Bray Curtis
bray_curtis_value = vegdist(species_vector_two_ecosystems,
method = "bray") %>%
as.numeric()
#Beta diversity: partitioning of beta diversity from Sorensen index into turnover (Simpson pair-wise dissimilarity) and nestedness (nestedness-fraction of Sorensen)
betapart_core_object = betapart.core(absence_presence_two_ecosystems)
beta_spatial_turnover_value = beta.pair(betapart_core_object)$beta.sim %>% as.double()
beta_nestedness_value = beta.pair(betapart_core_object)$beta.sne %>% as.double()
beta_total_value = beta.pair(betapart_core_object)$beta.sor %>% as.double()
#Gamma diversity: Meta-ecosystem richness
metaecosystem_richness_value = colSums(species_vector_two_ecosystems) %>%
specnumber()
#Put everything together
ds_metaecosystems[[row_n]] = ds_ecosystems %>%
filter(culture_ID %in% current_IDs,
time_point == time_point_input) %>%
summarise(
total_metaecosystem_bioarea_mm2 = sum(bioarea_tot_mm2),
total_metaecosystem_Ble_indiv = sum(Ble_tot_indiv),
total_metaecosystem_Cep_indiv = sum(Cep_tot_indiv),
total_metaecosystem_Col_indiv = sum(Col_tot_indiv),
total_metaecosystem_Eug_indiv = sum(Eug_tot_indiv),
total_metaecosystem_Eup_indiv = sum(Eup_tot_indiv),
total_metaecosystem_Lox_indiv = sum(Lox_tot_indiv),
total_metaecosystem_Pau_indiv = sum(Pau_tot_indiv),
total_metaecosystem_Pca_indiv = sum(Pca_tot_indiv),
total_metaecosystem_Spi_indiv = sum(Spi_tot_indiv),
total_metaecosystem_Spi_te_indiv = sum(Spi_te_tot_indiv),
total_metaecosystem_Tet_indiv = sum(Tet_tot_indiv)
) %>%
mutate(
system_nr = current_system_nr,
ecosystems_combined = current_combination,
metaecosystem_type = current_metaeco_type,
disturbance = current_disturbance,
time_point = time_point_input,
day = current_day,
jaccard_index = jaccard_index_value,
bray_curtis = bray_curtis_value,
beta_spatial_turnover = beta_spatial_turnover_value,
beta_nestedness = beta_nestedness_value,
beta_total = beta_total_value,
metaecosystem_richness = metaecosystem_richness_value,
mean_shannon = shannon_value,
mean_richness = mean_richness_value
) %>%
ungroup()
}
}## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): missing
## values in results## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"## Warning in vegdist(species_vector_two_ecosystems, method = "jaccard"): you have empty rows: their dissimilarities may be
## meaningless in method "jaccard"## Warning in vegdist(species_vector_two_ecosystems, method = "bray"): you have empty rows: their dissimilarities may be
## meaningless in method "bray"ds_metaecosystems = ds_metaecosystems %>%
bind_rows() %>%
as.data.frame() %>%
select(
time_point,
day,
system_nr,
ecosystems_combined,
disturbance,
metaecosystem_type,
mean_shannon,
mean_richness,
jaccard_index,
bray_curtis,
beta_spatial_turnover,
beta_nestedness,
beta_total,
metaecosystem_richness,
total_metaecosystem_bioarea_mm2,
paste0("total_metaecosystem_", protist_species, "_indiv")
)expect_equal(nrow(ds_metaecosystems),
n_time_points * n_ecosystems_combinations)#Add column connection
ds_metaecosystems$connection <-
ifelse(
ds_metaecosystems$metaecosystem_type %in% c("Medium-Medium unconnected",
"Small-Large unconnected"),
yes = "unconnected",
no = "connected"
)#Add column ecosystem size symmetry
ds_metaecosystems$ecosystem_size_symmetry <-
ifelse(
ds_metaecosystems$metaecosystem_type %in% c("Small-Large unconnected",
"Small-Large meta-ecosystem"),
yes = "asymmetric",
no = "symmetric"
)#Reorder the meta-ecosystems
ds_metaecosystems = ds_metaecosystems %>%
mutate(metaecosystem_type = factor(metaecosystem_type,
levels = metaecosystem_types_ordered))#Join ...
full_join(ds_metaecosystems,
unconnected_combinations_sets)## Warning in full_join(ds_metaecosystems, unconnected_combinations_sets): Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 1 of `x` matches multiple rows in `y`.
## ℹ Row 1 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
## "many-to-many"` to silence this warning.## time_point day system_nr ecosystems_combined disturbance
## 1 0 0 1001 1|11 low
## 2 0 0 1001 1|11 low
## 3 0 0 1001 1|11 low
## 4 0 0 1001 1|11 low
## 5 0 0 1001 1|11 low
## 6 0 0 1001 1|11 low
## 7 0 0 1001 1|11 low
## 8 0 0 1001 1|11 low
## 9 0 0 1001 1|11 low
## 10 0 0 1001 1|11 low
## 11 0 0 1001 1|11 low
## 12 0 0 1001 1|11 low
## 13 0 0 1001 1|11 low
## 14 0 0 1001 1|11 low
## 15 0 0 1001 1|11 low
## 16 0 0 1001 1|11 low
## 17 0 0 1001 1|11 low
## 18 0 0 1001 1|11 low
## 19 0 0 1001 1|11 low
## 20 0 0 1001 1|11 low
## 21 0 0 1001 1|11 low
## 22 0 0 1001 1|11 low
## 23 0 0 1001 1|11 low
## 24 0 0 1001 1|11 low
## 25 1 4 1001 1|11 low
## 26 1 4 1001 1|11 low
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## 3224 6 24 1017 4|12 low
## 3225 6 24 1017 4|12 low
## metaecosystem_type mean_shannon mean_richness jaccard_index
## 1 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3 Small-Large unconnected 2.0784670 11.0 0.0000000
## 4 Small-Large unconnected 2.0784670 11.0 0.0000000
## 5 Small-Large unconnected 2.0784670 11.0 0.0000000
## 6 Small-Large unconnected 2.0784670 11.0 0.0000000
## 7 Small-Large unconnected 2.0784670 11.0 0.0000000
## 8 Small-Large unconnected 2.0784670 11.0 0.0000000
## 9 Small-Large unconnected 2.0784670 11.0 0.0000000
## 10 Small-Large unconnected 2.0784670 11.0 0.0000000
## 11 Small-Large unconnected 2.0784670 11.0 0.0000000
## 12 Small-Large unconnected 2.0784670 11.0 0.0000000
## 13 Small-Large unconnected 2.0784670 11.0 0.0000000
## 14 Small-Large unconnected 2.0784670 11.0 0.0000000
## 15 Small-Large unconnected 2.0784670 11.0 0.0000000
## 16 Small-Large unconnected 2.0784670 11.0 0.0000000
## 17 Small-Large unconnected 2.0784670 11.0 0.0000000
## 18 Small-Large unconnected 2.0784670 11.0 0.0000000
## 19 Small-Large unconnected 2.0784670 11.0 0.0000000
## 20 Small-Large unconnected 2.0784670 11.0 0.0000000
## 21 Small-Large unconnected 2.0784670 11.0 0.0000000
## 22 Small-Large unconnected 2.0784670 11.0 0.0000000
## 23 Small-Large unconnected 2.0784670 11.0 0.0000000
## 24 Small-Large unconnected 2.0784670 11.0 0.0000000
## 25 Small-Large unconnected 1.5003642 7.5 0.3797327
## 26 Small-Large unconnected 1.5003642 7.5 0.3797327
## 27 Small-Large unconnected 1.5003642 7.5 0.3797327
## 28 Small-Large unconnected 1.5003642 7.5 0.3797327
## 29 Small-Large unconnected 1.5003642 7.5 0.3797327
## 30 Small-Large unconnected 1.5003642 7.5 0.3797327
## 31 Small-Large unconnected 1.5003642 7.5 0.3797327
## 32 Small-Large unconnected 1.5003642 7.5 0.3797327
## 33 Small-Large unconnected 1.5003642 7.5 0.3797327
## 34 Small-Large unconnected 1.5003642 7.5 0.3797327
## 35 Small-Large unconnected 1.5003642 7.5 0.3797327
## 36 Small-Large unconnected 1.5003642 7.5 0.3797327
## 37 Small-Large unconnected 1.5003642 7.5 0.3797327
## 38 Small-Large unconnected 1.5003642 7.5 0.3797327
## 39 Small-Large unconnected 1.5003642 7.5 0.3797327
## 40 Small-Large unconnected 1.5003642 7.5 0.3797327
## 41 Small-Large unconnected 1.5003642 7.5 0.3797327
## 42 Small-Large unconnected 1.5003642 7.5 0.3797327
## 43 Small-Large unconnected 1.5003642 7.5 0.3797327
## 44 Small-Large unconnected 1.5003642 7.5 0.3797327
## 45 Small-Large unconnected 1.5003642 7.5 0.3797327
## 46 Small-Large unconnected 1.5003642 7.5 0.3797327
## 47 Small-Large unconnected 1.5003642 7.5 0.3797327
## 48 Small-Large unconnected 1.5003642 7.5 0.3797327
## 49 Small-Large unconnected 1.5643953 8.0 0.5027346
## 50 Small-Large unconnected 1.5643953 8.0 0.5027346
## 51 Small-Large unconnected 1.5643953 8.0 0.5027346
## 52 Small-Large unconnected 1.5643953 8.0 0.5027346
## 53 Small-Large unconnected 1.5643953 8.0 0.5027346
## 54 Small-Large unconnected 1.5643953 8.0 0.5027346
## 55 Small-Large unconnected 1.5643953 8.0 0.5027346
## 56 Small-Large unconnected 1.5643953 8.0 0.5027346
## 57 Small-Large unconnected 1.5643953 8.0 0.5027346
## 58 Small-Large unconnected 1.5643953 8.0 0.5027346
## 59 Small-Large unconnected 1.5643953 8.0 0.5027346
## 60 Small-Large unconnected 1.5643953 8.0 0.5027346
## 61 Small-Large unconnected 1.5643953 8.0 0.5027346
## 62 Small-Large unconnected 1.5643953 8.0 0.5027346
## 63 Small-Large unconnected 1.5643953 8.0 0.5027346
## 64 Small-Large unconnected 1.5643953 8.0 0.5027346
## 65 Small-Large unconnected 1.5643953 8.0 0.5027346
## 66 Small-Large unconnected 1.5643953 8.0 0.5027346
## 67 Small-Large unconnected 1.5643953 8.0 0.5027346
## 68 Small-Large unconnected 1.5643953 8.0 0.5027346
## 69 Small-Large unconnected 1.5643953 8.0 0.5027346
## 70 Small-Large unconnected 1.5643953 8.0 0.5027346
## 71 Small-Large unconnected 1.5643953 8.0 0.5027346
## 72 Small-Large unconnected 1.5643953 8.0 0.5027346
## 73 Small-Large unconnected 1.6095690 6.0 0.8561835
## 74 Small-Large unconnected 1.6095690 6.0 0.8561835
## 75 Small-Large unconnected 1.6095690 6.0 0.8561835
## 76 Small-Large unconnected 1.6095690 6.0 0.8561835
## 77 Small-Large unconnected 1.6095690 6.0 0.8561835
## 78 Small-Large unconnected 1.6095690 6.0 0.8561835
## 79 Small-Large unconnected 1.6095690 6.0 0.8561835
## 80 Small-Large unconnected 1.6095690 6.0 0.8561835
## 81 Small-Large unconnected 1.6095690 6.0 0.8561835
## 82 Small-Large unconnected 1.6095690 6.0 0.8561835
## 83 Small-Large unconnected 1.6095690 6.0 0.8561835
## 84 Small-Large unconnected 1.6095690 6.0 0.8561835
## 85 Small-Large unconnected 1.6095690 6.0 0.8561835
## 86 Small-Large unconnected 1.6095690 6.0 0.8561835
## 87 Small-Large unconnected 1.6095690 6.0 0.8561835
## 88 Small-Large unconnected 1.6095690 6.0 0.8561835
## 89 Small-Large unconnected 1.6095690 6.0 0.8561835
## 90 Small-Large unconnected 1.6095690 6.0 0.8561835
## 91 Small-Large unconnected 1.6095690 6.0 0.8561835
## 92 Small-Large unconnected 1.6095690 6.0 0.8561835
## 93 Small-Large unconnected 1.6095690 6.0 0.8561835
## 94 Small-Large unconnected 1.6095690 6.0 0.8561835
## 95 Small-Large unconnected 1.6095690 6.0 0.8561835
## 96 Small-Large unconnected 1.6095690 6.0 0.8561835
## 97 Small-Large unconnected 1.8022460 7.5 0.4038401
## 98 Small-Large unconnected 1.8022460 7.5 0.4038401
## 99 Small-Large unconnected 1.8022460 7.5 0.4038401
## 100 Small-Large unconnected 1.8022460 7.5 0.4038401
## 101 Small-Large unconnected 1.8022460 7.5 0.4038401
## 102 Small-Large unconnected 1.8022460 7.5 0.4038401
## 103 Small-Large unconnected 1.8022460 7.5 0.4038401
## 104 Small-Large unconnected 1.8022460 7.5 0.4038401
## 105 Small-Large unconnected 1.8022460 7.5 0.4038401
## 106 Small-Large unconnected 1.8022460 7.5 0.4038401
## 107 Small-Large unconnected 1.8022460 7.5 0.4038401
## 108 Small-Large unconnected 1.8022460 7.5 0.4038401
## 109 Small-Large unconnected 1.8022460 7.5 0.4038401
## 110 Small-Large unconnected 1.8022460 7.5 0.4038401
## 111 Small-Large unconnected 1.8022460 7.5 0.4038401
## 112 Small-Large unconnected 1.8022460 7.5 0.4038401
## 113 Small-Large unconnected 1.8022460 7.5 0.4038401
## 114 Small-Large unconnected 1.8022460 7.5 0.4038401
## 115 Small-Large unconnected 1.8022460 7.5 0.4038401
## 116 Small-Large unconnected 1.8022460 7.5 0.4038401
## 117 Small-Large unconnected 1.8022460 7.5 0.4038401
## 118 Small-Large unconnected 1.8022460 7.5 0.4038401
## 119 Small-Large unconnected 1.8022460 7.5 0.4038401
## 120 Small-Large unconnected 1.8022460 7.5 0.4038401
## 121 Small-Large unconnected 0.9046531 4.0 0.8022244
## 122 Small-Large unconnected 0.9046531 4.0 0.8022244
## 123 Small-Large unconnected 0.9046531 4.0 0.8022244
## 124 Small-Large unconnected 0.9046531 4.0 0.8022244
## 125 Small-Large unconnected 0.9046531 4.0 0.8022244
## 126 Small-Large unconnected 0.9046531 4.0 0.8022244
## 127 Small-Large unconnected 0.9046531 4.0 0.8022244
## 128 Small-Large unconnected 0.9046531 4.0 0.8022244
## 129 Small-Large unconnected 0.9046531 4.0 0.8022244
## 130 Small-Large unconnected 0.9046531 4.0 0.8022244
## 131 Small-Large unconnected 0.9046531 4.0 0.8022244
## 132 Small-Large unconnected 0.9046531 4.0 0.8022244
## 133 Small-Large unconnected 0.9046531 4.0 0.8022244
## 134 Small-Large unconnected 0.9046531 4.0 0.8022244
## 135 Small-Large unconnected 0.9046531 4.0 0.8022244
## 136 Small-Large unconnected 0.9046531 4.0 0.8022244
## 137 Small-Large unconnected 0.9046531 4.0 0.8022244
## 138 Small-Large unconnected 0.9046531 4.0 0.8022244
## 139 Small-Large unconnected 0.9046531 4.0 0.8022244
## 140 Small-Large unconnected 0.9046531 4.0 0.8022244
## 141 Small-Large unconnected 0.9046531 4.0 0.8022244
## 142 Small-Large unconnected 0.9046531 4.0 0.8022244
## 143 Small-Large unconnected 0.9046531 4.0 0.8022244
## 144 Small-Large unconnected 0.9046531 4.0 0.8022244
## 145 Small-Large unconnected 1.1722772 6.0 0.8009542
## 146 Small-Large unconnected 1.1722772 6.0 0.8009542
## 147 Small-Large unconnected 1.1722772 6.0 0.8009542
## 148 Small-Large unconnected 1.1722772 6.0 0.8009542
## 149 Small-Large unconnected 1.1722772 6.0 0.8009542
## 150 Small-Large unconnected 1.1722772 6.0 0.8009542
## 151 Small-Large unconnected 1.1722772 6.0 0.8009542
## 152 Small-Large unconnected 1.1722772 6.0 0.8009542
## 153 Small-Large unconnected 1.1722772 6.0 0.8009542
## 154 Small-Large unconnected 1.1722772 6.0 0.8009542
## 155 Small-Large unconnected 1.1722772 6.0 0.8009542
## 156 Small-Large unconnected 1.1722772 6.0 0.8009542
## 157 Small-Large unconnected 1.1722772 6.0 0.8009542
## 158 Small-Large unconnected 1.1722772 6.0 0.8009542
## 159 Small-Large unconnected 1.1722772 6.0 0.8009542
## 160 Small-Large unconnected 1.1722772 6.0 0.8009542
## 161 Small-Large unconnected 1.1722772 6.0 0.8009542
## 162 Small-Large unconnected 1.1722772 6.0 0.8009542
## 163 Small-Large unconnected 1.1722772 6.0 0.8009542
## 164 Small-Large unconnected 1.1722772 6.0 0.8009542
## 165 Small-Large unconnected 1.1722772 6.0 0.8009542
## 166 Small-Large unconnected 1.1722772 6.0 0.8009542
## 167 Small-Large unconnected 1.1722772 6.0 0.8009542
## 168 Small-Large unconnected 1.1722772 6.0 0.8009542
## 169 Small-Large unconnected 0.9415572 5.5 0.9159832
## 170 Small-Large unconnected 0.9415572 5.5 0.9159832
## 171 Small-Large unconnected 0.9415572 5.5 0.9159832
## 172 Small-Large unconnected 0.9415572 5.5 0.9159832
## 173 Small-Large unconnected 0.9415572 5.5 0.9159832
## 174 Small-Large unconnected 0.9415572 5.5 0.9159832
## 175 Small-Large unconnected 0.9415572 5.5 0.9159832
## 176 Small-Large unconnected 0.9415572 5.5 0.9159832
## 177 Small-Large unconnected 0.9415572 5.5 0.9159832
## 178 Small-Large unconnected 0.9415572 5.5 0.9159832
## 179 Small-Large unconnected 0.9415572 5.5 0.9159832
## 180 Small-Large unconnected 0.9415572 5.5 0.9159832
## 181 Small-Large unconnected 0.9415572 5.5 0.9159832
## 182 Small-Large unconnected 0.9415572 5.5 0.9159832
## 183 Small-Large unconnected 0.9415572 5.5 0.9159832
## 184 Small-Large unconnected 0.9415572 5.5 0.9159832
## 185 Small-Large unconnected 0.9415572 5.5 0.9159832
## 186 Small-Large unconnected 0.9415572 5.5 0.9159832
## 187 Small-Large unconnected 0.9415572 5.5 0.9159832
## 188 Small-Large unconnected 0.9415572 5.5 0.9159832
## 189 Small-Large unconnected 0.9415572 5.5 0.9159832
## 190 Small-Large unconnected 0.9415572 5.5 0.9159832
## 191 Small-Large unconnected 0.9415572 5.5 0.9159832
## 192 Small-Large unconnected 0.9415572 5.5 0.9159832
## 193 Small-Large unconnected 2.0784670 11.0 0.0000000
## 194 Small-Large unconnected 2.0784670 11.0 0.0000000
## 195 Small-Large unconnected 2.0784670 11.0 0.0000000
## 196 Small-Large unconnected 2.0784670 11.0 0.0000000
## 197 Small-Large unconnected 2.0784670 11.0 0.0000000
## 198 Small-Large unconnected 2.0784670 11.0 0.0000000
## 199 Small-Large unconnected 2.0784670 11.0 0.0000000
## 200 Small-Large unconnected 2.0784670 11.0 0.0000000
## 201 Small-Large unconnected 2.0784670 11.0 0.0000000
## 202 Small-Large unconnected 2.0784670 11.0 0.0000000
## 203 Small-Large unconnected 2.0784670 11.0 0.0000000
## 204 Small-Large unconnected 2.0784670 11.0 0.0000000
## 205 Small-Large unconnected 2.0784670 11.0 0.0000000
## 206 Small-Large unconnected 2.0784670 11.0 0.0000000
## 207 Small-Large unconnected 2.0784670 11.0 0.0000000
## 208 Small-Large unconnected 2.0784670 11.0 0.0000000
## 209 Small-Large unconnected 2.0784670 11.0 0.0000000
## 210 Small-Large unconnected 2.0784670 11.0 0.0000000
## 211 Small-Large unconnected 2.0784670 11.0 0.0000000
## 212 Small-Large unconnected 2.0784670 11.0 0.0000000
## 213 Small-Large unconnected 2.0784670 11.0 0.0000000
## 214 Small-Large unconnected 2.0784670 11.0 0.0000000
## 215 Small-Large unconnected 2.0784670 11.0 0.0000000
## 216 Small-Large unconnected 2.0784670 11.0 0.0000000
## 217 Small-Large unconnected 1.7344675 8.0 0.5863882
## 218 Small-Large unconnected 1.7344675 8.0 0.5863882
## 219 Small-Large unconnected 1.7344675 8.0 0.5863882
## 220 Small-Large unconnected 1.7344675 8.0 0.5863882
## 221 Small-Large unconnected 1.7344675 8.0 0.5863882
## 222 Small-Large unconnected 1.7344675 8.0 0.5863882
## 223 Small-Large unconnected 1.7344675 8.0 0.5863882
## 224 Small-Large unconnected 1.7344675 8.0 0.5863882
## 225 Small-Large unconnected 1.7344675 8.0 0.5863882
## 226 Small-Large unconnected 1.7344675 8.0 0.5863882
## 227 Small-Large unconnected 1.7344675 8.0 0.5863882
## 228 Small-Large unconnected 1.7344675 8.0 0.5863882
## 229 Small-Large unconnected 1.7344675 8.0 0.5863882
## 230 Small-Large unconnected 1.7344675 8.0 0.5863882
## 231 Small-Large unconnected 1.7344675 8.0 0.5863882
## 232 Small-Large unconnected 1.7344675 8.0 0.5863882
## 233 Small-Large unconnected 1.7344675 8.0 0.5863882
## 234 Small-Large unconnected 1.7344675 8.0 0.5863882
## 235 Small-Large unconnected 1.7344675 8.0 0.5863882
## 236 Small-Large unconnected 1.7344675 8.0 0.5863882
## 237 Small-Large unconnected 1.7344675 8.0 0.5863882
## 238 Small-Large unconnected 1.7344675 8.0 0.5863882
## 239 Small-Large unconnected 1.7344675 8.0 0.5863882
## 240 Small-Large unconnected 1.7344675 8.0 0.5863882
## 241 Small-Large unconnected 1.4913521 6.5 0.4020438
## 242 Small-Large unconnected 1.4913521 6.5 0.4020438
## 243 Small-Large unconnected 1.4913521 6.5 0.4020438
## 244 Small-Large unconnected 1.4913521 6.5 0.4020438
## 245 Small-Large unconnected 1.4913521 6.5 0.4020438
## 246 Small-Large unconnected 1.4913521 6.5 0.4020438
## 247 Small-Large unconnected 1.4913521 6.5 0.4020438
## 248 Small-Large unconnected 1.4913521 6.5 0.4020438
## 249 Small-Large unconnected 1.4913521 6.5 0.4020438
## 250 Small-Large unconnected 1.4913521 6.5 0.4020438
## 251 Small-Large unconnected 1.4913521 6.5 0.4020438
## 252 Small-Large unconnected 1.4913521 6.5 0.4020438
## 253 Small-Large unconnected 1.4913521 6.5 0.4020438
## 254 Small-Large unconnected 1.4913521 6.5 0.4020438
## 255 Small-Large unconnected 1.4913521 6.5 0.4020438
## 256 Small-Large unconnected 1.4913521 6.5 0.4020438
## 257 Small-Large unconnected 1.4913521 6.5 0.4020438
## 258 Small-Large unconnected 1.4913521 6.5 0.4020438
## 259 Small-Large unconnected 1.4913521 6.5 0.4020438
## 260 Small-Large unconnected 1.4913521 6.5 0.4020438
## 261 Small-Large unconnected 1.4913521 6.5 0.4020438
## 262 Small-Large unconnected 1.4913521 6.5 0.4020438
## 263 Small-Large unconnected 1.4913521 6.5 0.4020438
## 264 Small-Large unconnected 1.4913521 6.5 0.4020438
## 265 Small-Large unconnected 1.5288340 6.0 0.9015342
## 266 Small-Large unconnected 1.5288340 6.0 0.9015342
## 267 Small-Large unconnected 1.5288340 6.0 0.9015342
## 268 Small-Large unconnected 1.5288340 6.0 0.9015342
## 269 Small-Large unconnected 1.5288340 6.0 0.9015342
## 270 Small-Large unconnected 1.5288340 6.0 0.9015342
## 271 Small-Large unconnected 1.5288340 6.0 0.9015342
## 272 Small-Large unconnected 1.5288340 6.0 0.9015342
## 273 Small-Large unconnected 1.5288340 6.0 0.9015342
## 274 Small-Large unconnected 1.5288340 6.0 0.9015342
## 275 Small-Large unconnected 1.5288340 6.0 0.9015342
## 276 Small-Large unconnected 1.5288340 6.0 0.9015342
## 277 Small-Large unconnected 1.5288340 6.0 0.9015342
## 278 Small-Large unconnected 1.5288340 6.0 0.9015342
## 279 Small-Large unconnected 1.5288340 6.0 0.9015342
## 280 Small-Large unconnected 1.5288340 6.0 0.9015342
## 281 Small-Large unconnected 1.5288340 6.0 0.9015342
## 282 Small-Large unconnected 1.5288340 6.0 0.9015342
## 283 Small-Large unconnected 1.5288340 6.0 0.9015342
## 284 Small-Large unconnected 1.5288340 6.0 0.9015342
## 285 Small-Large unconnected 1.5288340 6.0 0.9015342
## 286 Small-Large unconnected 1.5288340 6.0 0.9015342
## 287 Small-Large unconnected 1.5288340 6.0 0.9015342
## 288 Small-Large unconnected 1.5288340 6.0 0.9015342
## 289 Small-Large unconnected 1.5754616 6.0 0.5594016
## 290 Small-Large unconnected 1.5754616 6.0 0.5594016
## 291 Small-Large unconnected 1.5754616 6.0 0.5594016
## 292 Small-Large unconnected 1.5754616 6.0 0.5594016
## 293 Small-Large unconnected 1.5754616 6.0 0.5594016
## 294 Small-Large unconnected 1.5754616 6.0 0.5594016
## 295 Small-Large unconnected 1.5754616 6.0 0.5594016
## 296 Small-Large unconnected 1.5754616 6.0 0.5594016
## 297 Small-Large unconnected 1.5754616 6.0 0.5594016
## 298 Small-Large unconnected 1.5754616 6.0 0.5594016
## 299 Small-Large unconnected 1.5754616 6.0 0.5594016
## 300 Small-Large unconnected 1.5754616 6.0 0.5594016
## 301 Small-Large unconnected 1.5754616 6.0 0.5594016
## 302 Small-Large unconnected 1.5754616 6.0 0.5594016
## 303 Small-Large unconnected 1.5754616 6.0 0.5594016
## 304 Small-Large unconnected 1.5754616 6.0 0.5594016
## 305 Small-Large unconnected 1.5754616 6.0 0.5594016
## 306 Small-Large unconnected 1.5754616 6.0 0.5594016
## 307 Small-Large unconnected 1.5754616 6.0 0.5594016
## 308 Small-Large unconnected 1.5754616 6.0 0.5594016
## 309 Small-Large unconnected 1.5754616 6.0 0.5594016
## 310 Small-Large unconnected 1.5754616 6.0 0.5594016
## 311 Small-Large unconnected 1.5754616 6.0 0.5594016
## 312 Small-Large unconnected 1.5754616 6.0 0.5594016
## 313 Small-Large unconnected 1.1147692 5.0 0.7862454
## 314 Small-Large unconnected 1.1147692 5.0 0.7862454
## 315 Small-Large unconnected 1.1147692 5.0 0.7862454
## 316 Small-Large unconnected 1.1147692 5.0 0.7862454
## 317 Small-Large unconnected 1.1147692 5.0 0.7862454
## 318 Small-Large unconnected 1.1147692 5.0 0.7862454
## 319 Small-Large unconnected 1.1147692 5.0 0.7862454
## 320 Small-Large unconnected 1.1147692 5.0 0.7862454
## 321 Small-Large unconnected 1.1147692 5.0 0.7862454
## 322 Small-Large unconnected 1.1147692 5.0 0.7862454
## 323 Small-Large unconnected 1.1147692 5.0 0.7862454
## 324 Small-Large unconnected 1.1147692 5.0 0.7862454
## 325 Small-Large unconnected 1.1147692 5.0 0.7862454
## 326 Small-Large unconnected 1.1147692 5.0 0.7862454
## 327 Small-Large unconnected 1.1147692 5.0 0.7862454
## 328 Small-Large unconnected 1.1147692 5.0 0.7862454
## 329 Small-Large unconnected 1.1147692 5.0 0.7862454
## 330 Small-Large unconnected 1.1147692 5.0 0.7862454
## 331 Small-Large unconnected 1.1147692 5.0 0.7862454
## 332 Small-Large unconnected 1.1147692 5.0 0.7862454
## 333 Small-Large unconnected 1.1147692 5.0 0.7862454
## 334 Small-Large unconnected 1.1147692 5.0 0.7862454
## 335 Small-Large unconnected 1.1147692 5.0 0.7862454
## 336 Small-Large unconnected 1.1147692 5.0 0.7862454
## 337 Small-Large unconnected 1.2716771 6.0 0.7890579
## 338 Small-Large unconnected 1.2716771 6.0 0.7890579
## 339 Small-Large unconnected 1.2716771 6.0 0.7890579
## 340 Small-Large unconnected 1.2716771 6.0 0.7890579
## 341 Small-Large unconnected 1.2716771 6.0 0.7890579
## 342 Small-Large unconnected 1.2716771 6.0 0.7890579
## 343 Small-Large unconnected 1.2716771 6.0 0.7890579
## 344 Small-Large unconnected 1.2716771 6.0 0.7890579
## 345 Small-Large unconnected 1.2716771 6.0 0.7890579
## 346 Small-Large unconnected 1.2716771 6.0 0.7890579
## 347 Small-Large unconnected 1.2716771 6.0 0.7890579
## 348 Small-Large unconnected 1.2716771 6.0 0.7890579
## 349 Small-Large unconnected 1.2716771 6.0 0.7890579
## 350 Small-Large unconnected 1.2716771 6.0 0.7890579
## 351 Small-Large unconnected 1.2716771 6.0 0.7890579
## 352 Small-Large unconnected 1.2716771 6.0 0.7890579
## 353 Small-Large unconnected 1.2716771 6.0 0.7890579
## 354 Small-Large unconnected 1.2716771 6.0 0.7890579
## 355 Small-Large unconnected 1.2716771 6.0 0.7890579
## 356 Small-Large unconnected 1.2716771 6.0 0.7890579
## 357 Small-Large unconnected 1.2716771 6.0 0.7890579
## 358 Small-Large unconnected 1.2716771 6.0 0.7890579
## 359 Small-Large unconnected 1.2716771 6.0 0.7890579
## 360 Small-Large unconnected 1.2716771 6.0 0.7890579
## 361 Small-Large unconnected 1.0070034 4.5 0.9160517
## 362 Small-Large unconnected 1.0070034 4.5 0.9160517
## 363 Small-Large unconnected 1.0070034 4.5 0.9160517
## 364 Small-Large unconnected 1.0070034 4.5 0.9160517
## 365 Small-Large unconnected 1.0070034 4.5 0.9160517
## 366 Small-Large unconnected 1.0070034 4.5 0.9160517
## 367 Small-Large unconnected 1.0070034 4.5 0.9160517
## 368 Small-Large unconnected 1.0070034 4.5 0.9160517
## 369 Small-Large unconnected 1.0070034 4.5 0.9160517
## 370 Small-Large unconnected 1.0070034 4.5 0.9160517
## 371 Small-Large unconnected 1.0070034 4.5 0.9160517
## 372 Small-Large unconnected 1.0070034 4.5 0.9160517
## 373 Small-Large unconnected 1.0070034 4.5 0.9160517
## 374 Small-Large unconnected 1.0070034 4.5 0.9160517
## 375 Small-Large unconnected 1.0070034 4.5 0.9160517
## 376 Small-Large unconnected 1.0070034 4.5 0.9160517
## 377 Small-Large unconnected 1.0070034 4.5 0.9160517
## 378 Small-Large unconnected 1.0070034 4.5 0.9160517
## 379 Small-Large unconnected 1.0070034 4.5 0.9160517
## 380 Small-Large unconnected 1.0070034 4.5 0.9160517
## 381 Small-Large unconnected 1.0070034 4.5 0.9160517
## 382 Small-Large unconnected 1.0070034 4.5 0.9160517
## 383 Small-Large unconnected 1.0070034 4.5 0.9160517
## 384 Small-Large unconnected 1.0070034 4.5 0.9160517
## 385 Small-Large unconnected 2.0784670 11.0 0.0000000
## 386 Small-Large unconnected 2.0784670 11.0 0.0000000
## 387 Small-Large unconnected 2.0784670 11.0 0.0000000
## 388 Small-Large unconnected 2.0784670 11.0 0.0000000
## 389 Small-Large unconnected 2.0784670 11.0 0.0000000
## 390 Small-Large unconnected 2.0784670 11.0 0.0000000
## 391 Small-Large unconnected 2.0784670 11.0 0.0000000
## 392 Small-Large unconnected 2.0784670 11.0 0.0000000
## 393 Small-Large unconnected 2.0784670 11.0 0.0000000
## 394 Small-Large unconnected 2.0784670 11.0 0.0000000
## 395 Small-Large unconnected 2.0784670 11.0 0.0000000
## 396 Small-Large unconnected 2.0784670 11.0 0.0000000
## 397 Small-Large unconnected 2.0784670 11.0 0.0000000
## 398 Small-Large unconnected 2.0784670 11.0 0.0000000
## 399 Small-Large unconnected 2.0784670 11.0 0.0000000
## 400 Small-Large unconnected 2.0784670 11.0 0.0000000
## 401 Small-Large unconnected 2.0784670 11.0 0.0000000
## 402 Small-Large unconnected 2.0784670 11.0 0.0000000
## 403 Small-Large unconnected 2.0784670 11.0 0.0000000
## 404 Small-Large unconnected 2.0784670 11.0 0.0000000
## 405 Small-Large unconnected 2.0784670 11.0 0.0000000
## 406 Small-Large unconnected 2.0784670 11.0 0.0000000
## 407 Small-Large unconnected 2.0784670 11.0 0.0000000
## 408 Small-Large unconnected 2.0784670 11.0 0.0000000
## 409 Small-Large unconnected 1.6354094 8.0 0.5434531
## 410 Small-Large unconnected 1.6354094 8.0 0.5434531
## 411 Small-Large unconnected 1.6354094 8.0 0.5434531
## 412 Small-Large unconnected 1.6354094 8.0 0.5434531
## 413 Small-Large unconnected 1.6354094 8.0 0.5434531
## 414 Small-Large unconnected 1.6354094 8.0 0.5434531
## 415 Small-Large unconnected 1.6354094 8.0 0.5434531
## 416 Small-Large unconnected 1.6354094 8.0 0.5434531
## 417 Small-Large unconnected 1.6354094 8.0 0.5434531
## 418 Small-Large unconnected 1.6354094 8.0 0.5434531
## 419 Small-Large unconnected 1.6354094 8.0 0.5434531
## 420 Small-Large unconnected 1.6354094 8.0 0.5434531
## 421 Small-Large unconnected 1.6354094 8.0 0.5434531
## 422 Small-Large unconnected 1.6354094 8.0 0.5434531
## 423 Small-Large unconnected 1.6354094 8.0 0.5434531
## 424 Small-Large unconnected 1.6354094 8.0 0.5434531
## 425 Small-Large unconnected 1.6354094 8.0 0.5434531
## 426 Small-Large unconnected 1.6354094 8.0 0.5434531
## 427 Small-Large unconnected 1.6354094 8.0 0.5434531
## 428 Small-Large unconnected 1.6354094 8.0 0.5434531
## 429 Small-Large unconnected 1.6354094 8.0 0.5434531
## 430 Small-Large unconnected 1.6354094 8.0 0.5434531
## 431 Small-Large unconnected 1.6354094 8.0 0.5434531
## 432 Small-Large unconnected 1.6354094 8.0 0.5434531
## 433 Small-Large unconnected 1.7043816 8.5 0.4219277
## 434 Small-Large unconnected 1.7043816 8.5 0.4219277
## 435 Small-Large unconnected 1.7043816 8.5 0.4219277
## 436 Small-Large unconnected 1.7043816 8.5 0.4219277
## 437 Small-Large unconnected 1.7043816 8.5 0.4219277
## 438 Small-Large unconnected 1.7043816 8.5 0.4219277
## 439 Small-Large unconnected 1.7043816 8.5 0.4219277
## 440 Small-Large unconnected 1.7043816 8.5 0.4219277
## 441 Small-Large unconnected 1.7043816 8.5 0.4219277
## 442 Small-Large unconnected 1.7043816 8.5 0.4219277
## 443 Small-Large unconnected 1.7043816 8.5 0.4219277
## 444 Small-Large unconnected 1.7043816 8.5 0.4219277
## 445 Small-Large unconnected 1.7043816 8.5 0.4219277
## 446 Small-Large unconnected 1.7043816 8.5 0.4219277
## 447 Small-Large unconnected 1.7043816 8.5 0.4219277
## 448 Small-Large unconnected 1.7043816 8.5 0.4219277
## 449 Small-Large unconnected 1.7043816 8.5 0.4219277
## 450 Small-Large unconnected 1.7043816 8.5 0.4219277
## 451 Small-Large unconnected 1.7043816 8.5 0.4219277
## 452 Small-Large unconnected 1.7043816 8.5 0.4219277
## 453 Small-Large unconnected 1.7043816 8.5 0.4219277
## 454 Small-Large unconnected 1.7043816 8.5 0.4219277
## 455 Small-Large unconnected 1.7043816 8.5 0.4219277
## 456 Small-Large unconnected 1.7043816 8.5 0.4219277
## 457 Small-Large unconnected 1.6299430 6.5 0.8561835
## 458 Small-Large unconnected 1.6299430 6.5 0.8561835
## 459 Small-Large unconnected 1.6299430 6.5 0.8561835
## 460 Small-Large unconnected 1.6299430 6.5 0.8561835
## 461 Small-Large unconnected 1.6299430 6.5 0.8561835
## 462 Small-Large unconnected 1.6299430 6.5 0.8561835
## 463 Small-Large unconnected 1.6299430 6.5 0.8561835
## 464 Small-Large unconnected 1.6299430 6.5 0.8561835
## 465 Small-Large unconnected 1.6299430 6.5 0.8561835
## 466 Small-Large unconnected 1.6299430 6.5 0.8561835
## 467 Small-Large unconnected 1.6299430 6.5 0.8561835
## 468 Small-Large unconnected 1.6299430 6.5 0.8561835
## 469 Small-Large unconnected 1.6299430 6.5 0.8561835
## 470 Small-Large unconnected 1.6299430 6.5 0.8561835
## 471 Small-Large unconnected 1.6299430 6.5 0.8561835
## 472 Small-Large unconnected 1.6299430 6.5 0.8561835
## 473 Small-Large unconnected 1.6299430 6.5 0.8561835
## 474 Small-Large unconnected 1.6299430 6.5 0.8561835
## 475 Small-Large unconnected 1.6299430 6.5 0.8561835
## 476 Small-Large unconnected 1.6299430 6.5 0.8561835
## 477 Small-Large unconnected 1.6299430 6.5 0.8561835
## 478 Small-Large unconnected 1.6299430 6.5 0.8561835
## 479 Small-Large unconnected 1.6299430 6.5 0.8561835
## 480 Small-Large unconnected 1.6299430 6.5 0.8561835
## 481 Small-Large unconnected 1.7128054 7.0 0.5498951
## 482 Small-Large unconnected 1.7128054 7.0 0.5498951
## 483 Small-Large unconnected 1.7128054 7.0 0.5498951
## 484 Small-Large unconnected 1.7128054 7.0 0.5498951
## 485 Small-Large unconnected 1.7128054 7.0 0.5498951
## 486 Small-Large unconnected 1.7128054 7.0 0.5498951
## 487 Small-Large unconnected 1.7128054 7.0 0.5498951
## 488 Small-Large unconnected 1.7128054 7.0 0.5498951
## 489 Small-Large unconnected 1.7128054 7.0 0.5498951
## 490 Small-Large unconnected 1.7128054 7.0 0.5498951
## 491 Small-Large unconnected 1.7128054 7.0 0.5498951
## 492 Small-Large unconnected 1.7128054 7.0 0.5498951
## 493 Small-Large unconnected 1.7128054 7.0 0.5498951
## 494 Small-Large unconnected 1.7128054 7.0 0.5498951
## 495 Small-Large unconnected 1.7128054 7.0 0.5498951
## 496 Small-Large unconnected 1.7128054 7.0 0.5498951
## 497 Small-Large unconnected 1.7128054 7.0 0.5498951
## 498 Small-Large unconnected 1.7128054 7.0 0.5498951
## 499 Small-Large unconnected 1.7128054 7.0 0.5498951
## 500 Small-Large unconnected 1.7128054 7.0 0.5498951
## 501 Small-Large unconnected 1.7128054 7.0 0.5498951
## 502 Small-Large unconnected 1.7128054 7.0 0.5498951
## 503 Small-Large unconnected 1.7128054 7.0 0.5498951
## 504 Small-Large unconnected 1.7128054 7.0 0.5498951
## 505 Small-Large unconnected 0.9826256 4.0 0.8091603
## 506 Small-Large unconnected 0.9826256 4.0 0.8091603
## 507 Small-Large unconnected 0.9826256 4.0 0.8091603
## 508 Small-Large unconnected 0.9826256 4.0 0.8091603
## 509 Small-Large unconnected 0.9826256 4.0 0.8091603
## 510 Small-Large unconnected 0.9826256 4.0 0.8091603
## 511 Small-Large unconnected 0.9826256 4.0 0.8091603
## 512 Small-Large unconnected 0.9826256 4.0 0.8091603
## 513 Small-Large unconnected 0.9826256 4.0 0.8091603
## 514 Small-Large unconnected 0.9826256 4.0 0.8091603
## 515 Small-Large unconnected 0.9826256 4.0 0.8091603
## 516 Small-Large unconnected 0.9826256 4.0 0.8091603
## 517 Small-Large unconnected 0.9826256 4.0 0.8091603
## 518 Small-Large unconnected 0.9826256 4.0 0.8091603
## 519 Small-Large unconnected 0.9826256 4.0 0.8091603
## 520 Small-Large unconnected 0.9826256 4.0 0.8091603
## 521 Small-Large unconnected 0.9826256 4.0 0.8091603
## 522 Small-Large unconnected 0.9826256 4.0 0.8091603
## 523 Small-Large unconnected 0.9826256 4.0 0.8091603
## 524 Small-Large unconnected 0.9826256 4.0 0.8091603
## 525 Small-Large unconnected 0.9826256 4.0 0.8091603
## 526 Small-Large unconnected 0.9826256 4.0 0.8091603
## 527 Small-Large unconnected 0.9826256 4.0 0.8091603
## 528 Small-Large unconnected 0.9826256 4.0 0.8091603
## 529 Small-Large unconnected 1.1849855 6.5 0.7669141
## 530 Small-Large unconnected 1.1849855 6.5 0.7669141
## 531 Small-Large unconnected 1.1849855 6.5 0.7669141
## 532 Small-Large unconnected 1.1849855 6.5 0.7669141
## 533 Small-Large unconnected 1.1849855 6.5 0.7669141
## 534 Small-Large unconnected 1.1849855 6.5 0.7669141
## 535 Small-Large unconnected 1.1849855 6.5 0.7669141
## 536 Small-Large unconnected 1.1849855 6.5 0.7669141
## 537 Small-Large unconnected 1.1849855 6.5 0.7669141
## 538 Small-Large unconnected 1.1849855 6.5 0.7669141
## 539 Small-Large unconnected 1.1849855 6.5 0.7669141
## 540 Small-Large unconnected 1.1849855 6.5 0.7669141
## 541 Small-Large unconnected 1.1849855 6.5 0.7669141
## 542 Small-Large unconnected 1.1849855 6.5 0.7669141
## 543 Small-Large unconnected 1.1849855 6.5 0.7669141
## 544 Small-Large unconnected 1.1849855 6.5 0.7669141
## 545 Small-Large unconnected 1.1849855 6.5 0.7669141
## 546 Small-Large unconnected 1.1849855 6.5 0.7669141
## 547 Small-Large unconnected 1.1849855 6.5 0.7669141
## 548 Small-Large unconnected 1.1849855 6.5 0.7669141
## 549 Small-Large unconnected 1.1849855 6.5 0.7669141
## 550 Small-Large unconnected 1.1849855 6.5 0.7669141
## 551 Small-Large unconnected 1.1849855 6.5 0.7669141
## 552 Small-Large unconnected 1.1849855 6.5 0.7669141
## 553 Small-Large unconnected 0.8793394 4.5 0.9340896
## 554 Small-Large unconnected 0.8793394 4.5 0.9340896
## 555 Small-Large unconnected 0.8793394 4.5 0.9340896
## 556 Small-Large unconnected 0.8793394 4.5 0.9340896
## 557 Small-Large unconnected 0.8793394 4.5 0.9340896
## 558 Small-Large unconnected 0.8793394 4.5 0.9340896
## 559 Small-Large unconnected 0.8793394 4.5 0.9340896
## 560 Small-Large unconnected 0.8793394 4.5 0.9340896
## 561 Small-Large unconnected 0.8793394 4.5 0.9340896
## 562 Small-Large unconnected 0.8793394 4.5 0.9340896
## 563 Small-Large unconnected 0.8793394 4.5 0.9340896
## 564 Small-Large unconnected 0.8793394 4.5 0.9340896
## 565 Small-Large unconnected 0.8793394 4.5 0.9340896
## 566 Small-Large unconnected 0.8793394 4.5 0.9340896
## 567 Small-Large unconnected 0.8793394 4.5 0.9340896
## 568 Small-Large unconnected 0.8793394 4.5 0.9340896
## 569 Small-Large unconnected 0.8793394 4.5 0.9340896
## 570 Small-Large unconnected 0.8793394 4.5 0.9340896
## 571 Small-Large unconnected 0.8793394 4.5 0.9340896
## 572 Small-Large unconnected 0.8793394 4.5 0.9340896
## 573 Small-Large unconnected 0.8793394 4.5 0.9340896
## 574 Small-Large unconnected 0.8793394 4.5 0.9340896
## 575 Small-Large unconnected 0.8793394 4.5 0.9340896
## 576 Small-Large unconnected 0.8793394 4.5 0.9340896
## 577 Small-Large unconnected 2.0784670 11.0 0.0000000
## 578 Small-Large unconnected 2.0784670 11.0 0.0000000
## 579 Small-Large unconnected 2.0784670 11.0 0.0000000
## 580 Small-Large unconnected 2.0784670 11.0 0.0000000
## 581 Small-Large unconnected 2.0784670 11.0 0.0000000
## 582 Small-Large unconnected 2.0784670 11.0 0.0000000
## 583 Small-Large unconnected 2.0784670 11.0 0.0000000
## 584 Small-Large unconnected 2.0784670 11.0 0.0000000
## 585 Small-Large unconnected 2.0784670 11.0 0.0000000
## 586 Small-Large unconnected 2.0784670 11.0 0.0000000
## 587 Small-Large unconnected 2.0784670 11.0 0.0000000
## 588 Small-Large unconnected 2.0784670 11.0 0.0000000
## 589 Small-Large unconnected 2.0784670 11.0 0.0000000
## 590 Small-Large unconnected 2.0784670 11.0 0.0000000
## 591 Small-Large unconnected 2.0784670 11.0 0.0000000
## 592 Small-Large unconnected 2.0784670 11.0 0.0000000
## 593 Small-Large unconnected 2.0784670 11.0 0.0000000
## 594 Small-Large unconnected 2.0784670 11.0 0.0000000
## 595 Small-Large unconnected 2.0784670 11.0 0.0000000
## 596 Small-Large unconnected 2.0784670 11.0 0.0000000
## 597 Small-Large unconnected 2.0784670 11.0 0.0000000
## 598 Small-Large unconnected 2.0784670 11.0 0.0000000
## 599 Small-Large unconnected 2.0784670 11.0 0.0000000
## 600 Small-Large unconnected 2.0784670 11.0 0.0000000
## 601 Small-Large unconnected 1.5325570 7.0 0.6161471
## 602 Small-Large unconnected 1.5325570 7.0 0.6161471
## 603 Small-Large unconnected 1.5325570 7.0 0.6161471
## 604 Small-Large unconnected 1.5325570 7.0 0.6161471
## 605 Small-Large unconnected 1.5325570 7.0 0.6161471
## 606 Small-Large unconnected 1.5325570 7.0 0.6161471
## 607 Small-Large unconnected 1.5325570 7.0 0.6161471
## 608 Small-Large unconnected 1.5325570 7.0 0.6161471
## 609 Small-Large unconnected 1.5325570 7.0 0.6161471
## 610 Small-Large unconnected 1.5325570 7.0 0.6161471
## 611 Small-Large unconnected 1.5325570 7.0 0.6161471
## 612 Small-Large unconnected 1.5325570 7.0 0.6161471
## 613 Small-Large unconnected 1.5325570 7.0 0.6161471
## 614 Small-Large unconnected 1.5325570 7.0 0.6161471
## 615 Small-Large unconnected 1.5325570 7.0 0.6161471
## 616 Small-Large unconnected 1.5325570 7.0 0.6161471
## 617 Small-Large unconnected 1.5325570 7.0 0.6161471
## 618 Small-Large unconnected 1.5325570 7.0 0.6161471
## 619 Small-Large unconnected 1.5325570 7.0 0.6161471
## 620 Small-Large unconnected 1.5325570 7.0 0.6161471
## 621 Small-Large unconnected 1.5325570 7.0 0.6161471
## 622 Small-Large unconnected 1.5325570 7.0 0.6161471
## 623 Small-Large unconnected 1.5325570 7.0 0.6161471
## 624 Small-Large unconnected 1.5325570 7.0 0.6161471
## 625 Small-Large unconnected 1.5378489 8.0 0.5443405
## 626 Small-Large unconnected 1.5378489 8.0 0.5443405
## 627 Small-Large unconnected 1.5378489 8.0 0.5443405
## 628 Small-Large unconnected 1.5378489 8.0 0.5443405
## 629 Small-Large unconnected 1.5378489 8.0 0.5443405
## 630 Small-Large unconnected 1.5378489 8.0 0.5443405
## 631 Small-Large unconnected 1.5378489 8.0 0.5443405
## 632 Small-Large unconnected 1.5378489 8.0 0.5443405
## 633 Small-Large unconnected 1.5378489 8.0 0.5443405
## 634 Small-Large unconnected 1.5378489 8.0 0.5443405
## 635 Small-Large unconnected 1.5378489 8.0 0.5443405
## 636 Small-Large unconnected 1.5378489 8.0 0.5443405
## 637 Small-Large unconnected 1.5378489 8.0 0.5443405
## 638 Small-Large unconnected 1.5378489 8.0 0.5443405
## 639 Small-Large unconnected 1.5378489 8.0 0.5443405
## 640 Small-Large unconnected 1.5378489 8.0 0.5443405
## 641 Small-Large unconnected 1.5378489 8.0 0.5443405
## 642 Small-Large unconnected 1.5378489 8.0 0.5443405
## 643 Small-Large unconnected 1.5378489 8.0 0.5443405
## 644 Small-Large unconnected 1.5378489 8.0 0.5443405
## 645 Small-Large unconnected 1.5378489 8.0 0.5443405
## 646 Small-Large unconnected 1.5378489 8.0 0.5443405
## 647 Small-Large unconnected 1.5378489 8.0 0.5443405
## 648 Small-Large unconnected 1.5378489 8.0 0.5443405
## 649 Small-Large unconnected 1.2717353 5.0 0.8062622
## 650 Small-Large unconnected 1.2717353 5.0 0.8062622
## 651 Small-Large unconnected 1.2717353 5.0 0.8062622
## 652 Small-Large unconnected 1.2717353 5.0 0.8062622
## 653 Small-Large unconnected 1.2717353 5.0 0.8062622
## 654 Small-Large unconnected 1.2717353 5.0 0.8062622
## 655 Small-Large unconnected 1.2717353 5.0 0.8062622
## 656 Small-Large unconnected 1.2717353 5.0 0.8062622
## 657 Small-Large unconnected 1.2717353 5.0 0.8062622
## 658 Small-Large unconnected 1.2717353 5.0 0.8062622
## 659 Small-Large unconnected 1.2717353 5.0 0.8062622
## 660 Small-Large unconnected 1.2717353 5.0 0.8062622
## 661 Small-Large unconnected 1.2717353 5.0 0.8062622
## 662 Small-Large unconnected 1.2717353 5.0 0.8062622
## 663 Small-Large unconnected 1.2717353 5.0 0.8062622
## 664 Small-Large unconnected 1.2717353 5.0 0.8062622
## 665 Small-Large unconnected 1.2717353 5.0 0.8062622
## 666 Small-Large unconnected 1.2717353 5.0 0.8062622
## 667 Small-Large unconnected 1.2717353 5.0 0.8062622
## 668 Small-Large unconnected 1.2717353 5.0 0.8062622
## 669 Small-Large unconnected 1.2717353 5.0 0.8062622
## 670 Small-Large unconnected 1.2717353 5.0 0.8062622
## 671 Small-Large unconnected 1.2717353 5.0 0.8062622
## 672 Small-Large unconnected 1.2717353 5.0 0.8062622
## 673 Small-Large unconnected 1.5711195 6.5 0.5964585
## 674 Small-Large unconnected 1.5711195 6.5 0.5964585
## 675 Small-Large unconnected 1.5711195 6.5 0.5964585
## 676 Small-Large unconnected 1.5711195 6.5 0.5964585
## 677 Small-Large unconnected 1.5711195 6.5 0.5964585
## 678 Small-Large unconnected 1.5711195 6.5 0.5964585
## 679 Small-Large unconnected 1.5711195 6.5 0.5964585
## 680 Small-Large unconnected 1.5711195 6.5 0.5964585
## 681 Small-Large unconnected 1.5711195 6.5 0.5964585
## 682 Small-Large unconnected 1.5711195 6.5 0.5964585
## 683 Small-Large unconnected 1.5711195 6.5 0.5964585
## 684 Small-Large unconnected 1.5711195 6.5 0.5964585
## 685 Small-Large unconnected 1.5711195 6.5 0.5964585
## 686 Small-Large unconnected 1.5711195 6.5 0.5964585
## 687 Small-Large unconnected 1.5711195 6.5 0.5964585
## 688 Small-Large unconnected 1.5711195 6.5 0.5964585
## 689 Small-Large unconnected 1.5711195 6.5 0.5964585
## 690 Small-Large unconnected 1.5711195 6.5 0.5964585
## 691 Small-Large unconnected 1.5711195 6.5 0.5964585
## 692 Small-Large unconnected 1.5711195 6.5 0.5964585
## 693 Small-Large unconnected 1.5711195 6.5 0.5964585
## 694 Small-Large unconnected 1.5711195 6.5 0.5964585
## 695 Small-Large unconnected 1.5711195 6.5 0.5964585
## 696 Small-Large unconnected 1.5711195 6.5 0.5964585
## 697 Small-Large unconnected 0.9613777 3.5 0.7674121
## 698 Small-Large unconnected 0.9613777 3.5 0.7674121
## 699 Small-Large unconnected 0.9613777 3.5 0.7674121
## 700 Small-Large unconnected 0.9613777 3.5 0.7674121
## 701 Small-Large unconnected 0.9613777 3.5 0.7674121
## 702 Small-Large unconnected 0.9613777 3.5 0.7674121
## 703 Small-Large unconnected 0.9613777 3.5 0.7674121
## 704 Small-Large unconnected 0.9613777 3.5 0.7674121
## 705 Small-Large unconnected 0.9613777 3.5 0.7674121
## 706 Small-Large unconnected 0.9613777 3.5 0.7674121
## 707 Small-Large unconnected 0.9613777 3.5 0.7674121
## 708 Small-Large unconnected 0.9613777 3.5 0.7674121
## 709 Small-Large unconnected 0.9613777 3.5 0.7674121
## 710 Small-Large unconnected 0.9613777 3.5 0.7674121
## 711 Small-Large unconnected 0.9613777 3.5 0.7674121
## 712 Small-Large unconnected 0.9613777 3.5 0.7674121
## 713 Small-Large unconnected 0.9613777 3.5 0.7674121
## 714 Small-Large unconnected 0.9613777 3.5 0.7674121
## 715 Small-Large unconnected 0.9613777 3.5 0.7674121
## 716 Small-Large unconnected 0.9613777 3.5 0.7674121
## 717 Small-Large unconnected 0.9613777 3.5 0.7674121
## 718 Small-Large unconnected 0.9613777 3.5 0.7674121
## 719 Small-Large unconnected 0.9613777 3.5 0.7674121
## 720 Small-Large unconnected 0.9613777 3.5 0.7674121
## 721 Small-Large unconnected 1.3870793 5.5 0.6086957
## 722 Small-Large unconnected 1.3870793 5.5 0.6086957
## 723 Small-Large unconnected 1.3870793 5.5 0.6086957
## 724 Small-Large unconnected 1.3870793 5.5 0.6086957
## 725 Small-Large unconnected 1.3870793 5.5 0.6086957
## 726 Small-Large unconnected 1.3870793 5.5 0.6086957
## 727 Small-Large unconnected 1.3870793 5.5 0.6086957
## 728 Small-Large unconnected 1.3870793 5.5 0.6086957
## 729 Small-Large unconnected 1.3870793 5.5 0.6086957
## 730 Small-Large unconnected 1.3870793 5.5 0.6086957
## 731 Small-Large unconnected 1.3870793 5.5 0.6086957
## 732 Small-Large unconnected 1.3870793 5.5 0.6086957
## 733 Small-Large unconnected 1.3870793 5.5 0.6086957
## 734 Small-Large unconnected 1.3870793 5.5 0.6086957
## 735 Small-Large unconnected 1.3870793 5.5 0.6086957
## 736 Small-Large unconnected 1.3870793 5.5 0.6086957
## 737 Small-Large unconnected 1.3870793 5.5 0.6086957
## 738 Small-Large unconnected 1.3870793 5.5 0.6086957
## 739 Small-Large unconnected 1.3870793 5.5 0.6086957
## 740 Small-Large unconnected 1.3870793 5.5 0.6086957
## 741 Small-Large unconnected 1.3870793 5.5 0.6086957
## 742 Small-Large unconnected 1.3870793 5.5 0.6086957
## 743 Small-Large unconnected 1.3870793 5.5 0.6086957
## 744 Small-Large unconnected 1.3870793 5.5 0.6086957
## 745 Small-Large unconnected 0.9302665 3.5 0.6133333
## 746 Small-Large unconnected 0.9302665 3.5 0.6133333
## 747 Small-Large unconnected 0.9302665 3.5 0.6133333
## 748 Small-Large unconnected 0.9302665 3.5 0.6133333
## 749 Small-Large unconnected 0.9302665 3.5 0.6133333
## 750 Small-Large unconnected 0.9302665 3.5 0.6133333
## 751 Small-Large unconnected 0.9302665 3.5 0.6133333
## 752 Small-Large unconnected 0.9302665 3.5 0.6133333
## 753 Small-Large unconnected 0.9302665 3.5 0.6133333
## 754 Small-Large unconnected 0.9302665 3.5 0.6133333
## 755 Small-Large unconnected 0.9302665 3.5 0.6133333
## 756 Small-Large unconnected 0.9302665 3.5 0.6133333
## 757 Small-Large unconnected 0.9302665 3.5 0.6133333
## 758 Small-Large unconnected 0.9302665 3.5 0.6133333
## 759 Small-Large unconnected 0.9302665 3.5 0.6133333
## 760 Small-Large unconnected 0.9302665 3.5 0.6133333
## 761 Small-Large unconnected 0.9302665 3.5 0.6133333
## 762 Small-Large unconnected 0.9302665 3.5 0.6133333
## 763 Small-Large unconnected 0.9302665 3.5 0.6133333
## 764 Small-Large unconnected 0.9302665 3.5 0.6133333
## 765 Small-Large unconnected 0.9302665 3.5 0.6133333
## 766 Small-Large unconnected 0.9302665 3.5 0.6133333
## 767 Small-Large unconnected 0.9302665 3.5 0.6133333
## 768 Small-Large unconnected 0.9302665 3.5 0.6133333
## 769 Small-Large unconnected 2.0784670 11.0 0.0000000
## 770 Small-Large unconnected 2.0784670 11.0 0.0000000
## 771 Small-Large unconnected 2.0784670 11.0 0.0000000
## 772 Small-Large unconnected 2.0784670 11.0 0.0000000
## 773 Small-Large unconnected 2.0784670 11.0 0.0000000
## 774 Small-Large unconnected 2.0784670 11.0 0.0000000
## 775 Small-Large unconnected 2.0784670 11.0 0.0000000
## 776 Small-Large unconnected 2.0784670 11.0 0.0000000
## 777 Small-Large unconnected 2.0784670 11.0 0.0000000
## 778 Small-Large unconnected 2.0784670 11.0 0.0000000
## 779 Small-Large unconnected 2.0784670 11.0 0.0000000
## 780 Small-Large unconnected 2.0784670 11.0 0.0000000
## 781 Small-Large unconnected 2.0784670 11.0 0.0000000
## 782 Small-Large unconnected 2.0784670 11.0 0.0000000
## 783 Small-Large unconnected 2.0784670 11.0 0.0000000
## 784 Small-Large unconnected 2.0784670 11.0 0.0000000
## 785 Small-Large unconnected 2.0784670 11.0 0.0000000
## 786 Small-Large unconnected 2.0784670 11.0 0.0000000
## 787 Small-Large unconnected 2.0784670 11.0 0.0000000
## 788 Small-Large unconnected 2.0784670 11.0 0.0000000
## 789 Small-Large unconnected 2.0784670 11.0 0.0000000
## 790 Small-Large unconnected 2.0784670 11.0 0.0000000
## 791 Small-Large unconnected 2.0784670 11.0 0.0000000
## 792 Small-Large unconnected 2.0784670 11.0 0.0000000
## 793 Small-Large unconnected 1.7576182 8.0 0.6485050
## 794 Small-Large unconnected 1.7576182 8.0 0.6485050
## 795 Small-Large unconnected 1.7576182 8.0 0.6485050
## 796 Small-Large unconnected 1.7576182 8.0 0.6485050
## 797 Small-Large unconnected 1.7576182 8.0 0.6485050
## 798 Small-Large unconnected 1.7576182 8.0 0.6485050
## 799 Small-Large unconnected 1.7576182 8.0 0.6485050
## 800 Small-Large unconnected 1.7576182 8.0 0.6485050
## 801 Small-Large unconnected 1.7576182 8.0 0.6485050
## 802 Small-Large unconnected 1.7576182 8.0 0.6485050
## 803 Small-Large unconnected 1.7576182 8.0 0.6485050
## 804 Small-Large unconnected 1.7576182 8.0 0.6485050
## 805 Small-Large unconnected 1.7576182 8.0 0.6485050
## 806 Small-Large unconnected 1.7576182 8.0 0.6485050
## 807 Small-Large unconnected 1.7576182 8.0 0.6485050
## 808 Small-Large unconnected 1.7576182 8.0 0.6485050
## 809 Small-Large unconnected 1.7576182 8.0 0.6485050
## 810 Small-Large unconnected 1.7576182 8.0 0.6485050
## 811 Small-Large unconnected 1.7576182 8.0 0.6485050
## 812 Small-Large unconnected 1.7576182 8.0 0.6485050
## 813 Small-Large unconnected 1.7576182 8.0 0.6485050
## 814 Small-Large unconnected 1.7576182 8.0 0.6485050
## 815 Small-Large unconnected 1.7576182 8.0 0.6485050
## 816 Small-Large unconnected 1.7576182 8.0 0.6485050
## 817 Small-Large unconnected 1.6208829 7.5 0.5405548
## 818 Small-Large unconnected 1.6208829 7.5 0.5405548
## 819 Small-Large unconnected 1.6208829 7.5 0.5405548
## 820 Small-Large unconnected 1.6208829 7.5 0.5405548
## 821 Small-Large unconnected 1.6208829 7.5 0.5405548
## 822 Small-Large unconnected 1.6208829 7.5 0.5405548
## 823 Small-Large unconnected 1.6208829 7.5 0.5405548
## 824 Small-Large unconnected 1.6208829 7.5 0.5405548
## 825 Small-Large unconnected 1.6208829 7.5 0.5405548
## 826 Small-Large unconnected 1.6208829 7.5 0.5405548
## 827 Small-Large unconnected 1.6208829 7.5 0.5405548
## 828 Small-Large unconnected 1.6208829 7.5 0.5405548
## 829 Small-Large unconnected 1.6208829 7.5 0.5405548
## 830 Small-Large unconnected 1.6208829 7.5 0.5405548
## 831 Small-Large unconnected 1.6208829 7.5 0.5405548
## 832 Small-Large unconnected 1.6208829 7.5 0.5405548
## 833 Small-Large unconnected 1.6208829 7.5 0.5405548
## 834 Small-Large unconnected 1.6208829 7.5 0.5405548
## 835 Small-Large unconnected 1.6208829 7.5 0.5405548
## 836 Small-Large unconnected 1.6208829 7.5 0.5405548
## 837 Small-Large unconnected 1.6208829 7.5 0.5405548
## 838 Small-Large unconnected 1.6208829 7.5 0.5405548
## 839 Small-Large unconnected 1.6208829 7.5 0.5405548
## 840 Small-Large unconnected 1.6208829 7.5 0.5405548
## 841 Small-Large unconnected 1.5861251 6.0 0.8562784
## 842 Small-Large unconnected 1.5861251 6.0 0.8562784
## 843 Small-Large unconnected 1.5861251 6.0 0.8562784
## 844 Small-Large unconnected 1.5861251 6.0 0.8562784
## 845 Small-Large unconnected 1.5861251 6.0 0.8562784
## 846 Small-Large unconnected 1.5861251 6.0 0.8562784
## 847 Small-Large unconnected 1.5861251 6.0 0.8562784
## 848 Small-Large unconnected 1.5861251 6.0 0.8562784
## 849 Small-Large unconnected 1.5861251 6.0 0.8562784
## 850 Small-Large unconnected 1.5861251 6.0 0.8562784
## 851 Small-Large unconnected 1.5861251 6.0 0.8562784
## 852 Small-Large unconnected 1.5861251 6.0 0.8562784
## 853 Small-Large unconnected 1.5861251 6.0 0.8562784
## 854 Small-Large unconnected 1.5861251 6.0 0.8562784
## 855 Small-Large unconnected 1.5861251 6.0 0.8562784
## 856 Small-Large unconnected 1.5861251 6.0 0.8562784
## 857 Small-Large unconnected 1.5861251 6.0 0.8562784
## 858 Small-Large unconnected 1.5861251 6.0 0.8562784
## 859 Small-Large unconnected 1.5861251 6.0 0.8562784
## 860 Small-Large unconnected 1.5861251 6.0 0.8562784
## 861 Small-Large unconnected 1.5861251 6.0 0.8562784
## 862 Small-Large unconnected 1.5861251 6.0 0.8562784
## 863 Small-Large unconnected 1.5861251 6.0 0.8562784
## 864 Small-Large unconnected 1.5861251 6.0 0.8562784
## 865 Small-Large unconnected 1.6705149 7.5 0.5076640
## 866 Small-Large unconnected 1.6705149 7.5 0.5076640
## 867 Small-Large unconnected 1.6705149 7.5 0.5076640
## 868 Small-Large unconnected 1.6705149 7.5 0.5076640
## 869 Small-Large unconnected 1.6705149 7.5 0.5076640
## 870 Small-Large unconnected 1.6705149 7.5 0.5076640
## 871 Small-Large unconnected 1.6705149 7.5 0.5076640
## 872 Small-Large unconnected 1.6705149 7.5 0.5076640
## 873 Small-Large unconnected 1.6705149 7.5 0.5076640
## 874 Small-Large unconnected 1.6705149 7.5 0.5076640
## 875 Small-Large unconnected 1.6705149 7.5 0.5076640
## 876 Small-Large unconnected 1.6705149 7.5 0.5076640
## 877 Small-Large unconnected 1.6705149 7.5 0.5076640
## 878 Small-Large unconnected 1.6705149 7.5 0.5076640
## 879 Small-Large unconnected 1.6705149 7.5 0.5076640
## 880 Small-Large unconnected 1.6705149 7.5 0.5076640
## 881 Small-Large unconnected 1.6705149 7.5 0.5076640
## 882 Small-Large unconnected 1.6705149 7.5 0.5076640
## 883 Small-Large unconnected 1.6705149 7.5 0.5076640
## 884 Small-Large unconnected 1.6705149 7.5 0.5076640
## 885 Small-Large unconnected 1.6705149 7.5 0.5076640
## 886 Small-Large unconnected 1.6705149 7.5 0.5076640
## 887 Small-Large unconnected 1.6705149 7.5 0.5076640
## 888 Small-Large unconnected 1.6705149 7.5 0.5076640
## 889 Small-Large unconnected 1.1807457 5.0 0.8075314
## 890 Small-Large unconnected 1.1807457 5.0 0.8075314
## 891 Small-Large unconnected 1.1807457 5.0 0.8075314
## 892 Small-Large unconnected 1.1807457 5.0 0.8075314
## 893 Small-Large unconnected 1.1807457 5.0 0.8075314
## 894 Small-Large unconnected 1.1807457 5.0 0.8075314
## 895 Small-Large unconnected 1.1807457 5.0 0.8075314
## 896 Small-Large unconnected 1.1807457 5.0 0.8075314
## 897 Small-Large unconnected 1.1807457 5.0 0.8075314
## 898 Small-Large unconnected 1.1807457 5.0 0.8075314
## 899 Small-Large unconnected 1.1807457 5.0 0.8075314
## 900 Small-Large unconnected 1.1807457 5.0 0.8075314
## 901 Small-Large unconnected 1.1807457 5.0 0.8075314
## 902 Small-Large unconnected 1.1807457 5.0 0.8075314
## 903 Small-Large unconnected 1.1807457 5.0 0.8075314
## 904 Small-Large unconnected 1.1807457 5.0 0.8075314
## 905 Small-Large unconnected 1.1807457 5.0 0.8075314
## 906 Small-Large unconnected 1.1807457 5.0 0.8075314
## 907 Small-Large unconnected 1.1807457 5.0 0.8075314
## 908 Small-Large unconnected 1.1807457 5.0 0.8075314
## 909 Small-Large unconnected 1.1807457 5.0 0.8075314
## 910 Small-Large unconnected 1.1807457 5.0 0.8075314
## 911 Small-Large unconnected 1.1807457 5.0 0.8075314
## 912 Small-Large unconnected 1.1807457 5.0 0.8075314
## 913 Small-Large unconnected 1.5071598 6.5 0.8093303
## 914 Small-Large unconnected 1.5071598 6.5 0.8093303
## 915 Small-Large unconnected 1.5071598 6.5 0.8093303
## 916 Small-Large unconnected 1.5071598 6.5 0.8093303
## 917 Small-Large unconnected 1.5071598 6.5 0.8093303
## 918 Small-Large unconnected 1.5071598 6.5 0.8093303
## 919 Small-Large unconnected 1.5071598 6.5 0.8093303
## 920 Small-Large unconnected 1.5071598 6.5 0.8093303
## 921 Small-Large unconnected 1.5071598 6.5 0.8093303
## 922 Small-Large unconnected 1.5071598 6.5 0.8093303
## 923 Small-Large unconnected 1.5071598 6.5 0.8093303
## 924 Small-Large unconnected 1.5071598 6.5 0.8093303
## 925 Small-Large unconnected 1.5071598 6.5 0.8093303
## 926 Small-Large unconnected 1.5071598 6.5 0.8093303
## 927 Small-Large unconnected 1.5071598 6.5 0.8093303
## 928 Small-Large unconnected 1.5071598 6.5 0.8093303
## 929 Small-Large unconnected 1.5071598 6.5 0.8093303
## 930 Small-Large unconnected 1.5071598 6.5 0.8093303
## 931 Small-Large unconnected 1.5071598 6.5 0.8093303
## 932 Small-Large unconnected 1.5071598 6.5 0.8093303
## 933 Small-Large unconnected 1.5071598 6.5 0.8093303
## 934 Small-Large unconnected 1.5071598 6.5 0.8093303
## 935 Small-Large unconnected 1.5071598 6.5 0.8093303
## 936 Small-Large unconnected 1.5071598 6.5 0.8093303
## 937 Small-Large unconnected 0.9391687 5.0 0.9203269
## 938 Small-Large unconnected 0.9391687 5.0 0.9203269
## 939 Small-Large unconnected 0.9391687 5.0 0.9203269
## 940 Small-Large unconnected 0.9391687 5.0 0.9203269
## 941 Small-Large unconnected 0.9391687 5.0 0.9203269
## 942 Small-Large unconnected 0.9391687 5.0 0.9203269
## 943 Small-Large unconnected 0.9391687 5.0 0.9203269
## 944 Small-Large unconnected 0.9391687 5.0 0.9203269
## 945 Small-Large unconnected 0.9391687 5.0 0.9203269
## 946 Small-Large unconnected 0.9391687 5.0 0.9203269
## 947 Small-Large unconnected 0.9391687 5.0 0.9203269
## 948 Small-Large unconnected 0.9391687 5.0 0.9203269
## 949 Small-Large unconnected 0.9391687 5.0 0.9203269
## 950 Small-Large unconnected 0.9391687 5.0 0.9203269
## 951 Small-Large unconnected 0.9391687 5.0 0.9203269
## 952 Small-Large unconnected 0.9391687 5.0 0.9203269
## 953 Small-Large unconnected 0.9391687 5.0 0.9203269
## 954 Small-Large unconnected 0.9391687 5.0 0.9203269
## 955 Small-Large unconnected 0.9391687 5.0 0.9203269
## 956 Small-Large unconnected 0.9391687 5.0 0.9203269
## 957 Small-Large unconnected 0.9391687 5.0 0.9203269
## 958 Small-Large unconnected 0.9391687 5.0 0.9203269
## 959 Small-Large unconnected 0.9391687 5.0 0.9203269
## 960 Small-Large unconnected 0.9391687 5.0 0.9203269
## 961 Small-Large unconnected 2.0784670 11.0 0.0000000
## 962 Small-Large unconnected 2.0784670 11.0 0.0000000
## 963 Small-Large unconnected 2.0784670 11.0 0.0000000
## 964 Small-Large unconnected 2.0784670 11.0 0.0000000
## 965 Small-Large unconnected 2.0784670 11.0 0.0000000
## 966 Small-Large unconnected 2.0784670 11.0 0.0000000
## 967 Small-Large unconnected 2.0784670 11.0 0.0000000
## 968 Small-Large unconnected 2.0784670 11.0 0.0000000
## 969 Small-Large unconnected 2.0784670 11.0 0.0000000
## 970 Small-Large unconnected 2.0784670 11.0 0.0000000
## 971 Small-Large unconnected 2.0784670 11.0 0.0000000
## 972 Small-Large unconnected 2.0784670 11.0 0.0000000
## 973 Small-Large unconnected 2.0784670 11.0 0.0000000
## 974 Small-Large unconnected 2.0784670 11.0 0.0000000
## 975 Small-Large unconnected 2.0784670 11.0 0.0000000
## 976 Small-Large unconnected 2.0784670 11.0 0.0000000
## 977 Small-Large unconnected 2.0784670 11.0 0.0000000
## 978 Small-Large unconnected 2.0784670 11.0 0.0000000
## 979 Small-Large unconnected 2.0784670 11.0 0.0000000
## 980 Small-Large unconnected 2.0784670 11.0 0.0000000
## 981 Small-Large unconnected 2.0784670 11.0 0.0000000
## 982 Small-Large unconnected 2.0784670 11.0 0.0000000
## 983 Small-Large unconnected 2.0784670 11.0 0.0000000
## 984 Small-Large unconnected 2.0784670 11.0 0.0000000
## 985 Small-Large unconnected 1.5540186 8.0 0.4775502
## 986 Small-Large unconnected 1.5540186 8.0 0.4775502
## 987 Small-Large unconnected 1.5540186 8.0 0.4775502
## 988 Small-Large unconnected 1.5540186 8.0 0.4775502
## 989 Small-Large unconnected 1.5540186 8.0 0.4775502
## 990 Small-Large unconnected 1.5540186 8.0 0.4775502
## 991 Small-Large unconnected 1.5540186 8.0 0.4775502
## 992 Small-Large unconnected 1.5540186 8.0 0.4775502
## 993 Small-Large unconnected 1.5540186 8.0 0.4775502
## 994 Small-Large unconnected 1.5540186 8.0 0.4775502
## 995 Small-Large unconnected 1.5540186 8.0 0.4775502
## 996 Small-Large unconnected 1.5540186 8.0 0.4775502
## 997 Small-Large unconnected 1.5540186 8.0 0.4775502
## 998 Small-Large unconnected 1.5540186 8.0 0.4775502
## 999 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1000 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1001 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1002 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1003 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1004 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1005 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1006 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1007 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1008 Small-Large unconnected 1.5540186 8.0 0.4775502
## 1009 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1010 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1011 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1012 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1013 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1014 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1015 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1016 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1017 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1018 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1019 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1020 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1021 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1022 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1023 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1024 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1025 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1026 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1027 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1028 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1029 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1030 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1031 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1032 Small-Large unconnected 1.5213817 8.5 0.6802785
## 1033 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1034 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1035 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1036 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1037 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1038 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1039 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1040 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1041 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1042 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1043 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1044 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1045 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1046 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1047 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1048 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1049 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1050 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1051 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1052 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1053 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1054 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1055 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1056 Small-Large unconnected 1.7632593 7.0 0.4519279
## 1057 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1058 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1059 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1060 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1061 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1062 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1063 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1064 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1065 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1066 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1067 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1068 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1069 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1070 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1071 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1072 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1073 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1074 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1075 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1076 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1077 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1078 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1079 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1080 Small-Large unconnected 1.3837136 5.5 0.6129142
## 1081 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1082 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1083 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1084 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1085 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1086 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1087 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1088 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1089 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1090 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1091 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1092 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1093 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1094 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1095 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1096 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1097 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1098 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1099 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1100 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1101 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1102 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1103 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1104 Small-Large unconnected 1.1906786 4.5 0.9314463
## 1105 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1106 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1107 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1108 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1109 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1110 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1111 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1112 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1113 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1114 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1115 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1116 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1117 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1118 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1119 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1120 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1121 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1122 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1123 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1124 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1125 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1126 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1127 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1128 Small-Large unconnected 0.5580146 4.0 0.8940736
## 1129 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1130 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1131 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1132 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1133 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1134 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1135 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1136 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1137 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1138 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1139 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1140 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1141 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1142 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1143 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1144 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1145 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1146 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1147 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1148 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1149 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1150 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1151 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1152 Small-Large unconnected 0.6573424 5.0 0.9461440
## 1153 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1154 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1155 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1156 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1157 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1158 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1159 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1160 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1161 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1162 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1163 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1164 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1165 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1166 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1167 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1168 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1169 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1170 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1171 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1172 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1173 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1174 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1175 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1176 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1177 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1178 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1179 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1180 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1181 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1182 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1183 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1184 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1185 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1186 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1187 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1188 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1189 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1190 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1191 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1192 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1193 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1194 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1195 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1196 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1197 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1198 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1199 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1200 Small-Large unconnected 1.7881218 8.5 0.4851643
## 1201 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1202 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1203 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1204 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1205 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1206 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1207 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1208 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1209 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1210 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1211 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1212 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1213 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1214 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1215 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1216 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1217 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1218 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1219 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1220 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1221 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1222 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1223 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1224 Small-Large unconnected 1.4483385 7.0 0.6127187
## 1225 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1226 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1227 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1228 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1229 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1230 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1231 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1232 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1233 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1234 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1235 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1236 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1237 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1238 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1239 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1240 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1241 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1242 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1243 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1244 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1245 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1246 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1247 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1248 Small-Large unconnected 1.6825243 7.0 0.5191233
## 1249 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1250 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1251 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1252 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1253 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1254 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1255 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1256 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1257 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1258 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1259 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1260 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1261 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1262 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1263 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1264 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1265 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1266 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1267 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1268 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1269 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1270 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1271 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1272 Small-Large unconnected 1.1569293 4.0 0.7495992
## 1273 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1274 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1275 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1276 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1277 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1278 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1279 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1280 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1281 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1282 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1283 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1284 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1285 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1286 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1287 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1288 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1289 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1290 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1291 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1292 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1293 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1294 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1295 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1296 Small-Large unconnected 1.4007946 5.5 0.8509009
## 1297 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1298 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1299 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1300 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1301 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1302 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1303 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1304 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1305 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1306 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1307 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1308 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1309 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1310 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1311 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1312 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1313 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1314 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1315 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1316 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1317 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1318 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1319 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1320 Small-Large unconnected 0.6574145 4.0 0.8908058
## 1321 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1322 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1323 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1324 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1325 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1326 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1327 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1328 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1329 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1330 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1331 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1332 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1333 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1334 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1335 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1336 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1337 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1338 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1339 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1340 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1341 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1342 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1343 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1344 Small-Large unconnected 0.7227886 4.0 0.9301829
## 1345 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1346 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1347 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1348 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1349 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1350 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1351 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1352 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1353 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1354 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1355 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1356 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1357 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1358 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1359 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1360 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1361 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1362 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1363 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1364 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1365 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1366 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1367 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1368 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1369 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1370 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1371 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1372 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1373 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1374 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1375 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1376 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1377 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1378 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1379 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1380 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1381 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1382 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1383 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1384 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1385 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1386 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1387 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1388 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1389 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1390 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1391 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1392 Small-Large unconnected 1.6890637 8.5 0.5151939
## 1393 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1394 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1395 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1396 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1397 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1398 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1399 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1400 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1401 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1402 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1403 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1404 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1405 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1406 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1407 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1408 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1409 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1410 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1411 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1412 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1413 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1414 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1415 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1416 Small-Large unconnected 1.6613680 9.0 0.6067317
## 1417 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1418 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1419 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1420 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1421 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1422 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1423 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1424 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1425 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1426 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1427 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1428 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1429 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1430 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1431 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1432 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1433 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1434 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1435 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1436 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1437 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1438 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1439 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1440 Small-Large unconnected 1.7836333 7.5 0.5057999
## 1441 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1442 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1443 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1444 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1445 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1446 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1447 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1448 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1449 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1450 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1451 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1452 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1453 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1454 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1455 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1456 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1457 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1458 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1459 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1460 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1461 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1462 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1463 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1464 Small-Large unconnected 1.2942730 5.0 0.7453294
## 1465 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1466 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1467 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1468 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1469 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1470 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1471 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1472 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1473 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1474 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1475 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1476 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1477 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1478 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1479 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1480 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1481 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1482 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1483 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1484 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1485 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1486 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1487 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1488 Small-Large unconnected 1.2686511 4.5 0.9064490
## 1489 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1490 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1491 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1492 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1493 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1494 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1495 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1496 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1497 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1498 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1499 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1500 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1501 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1502 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1503 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1504 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1505 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1506 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1507 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1508 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1509 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1510 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1511 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1512 Small-Large unconnected 0.5707230 4.5 0.8832972
## 1513 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1514 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1515 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1516 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1517 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1518 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1519 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1520 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1521 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1522 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1523 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1524 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1525 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1526 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1527 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1528 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1529 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1530 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1531 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1532 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1533 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1534 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1535 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1536 Small-Large unconnected 0.5951247 4.0 0.9576002
## 1537 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1538 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1539 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1540 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1541 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1542 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1543 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1544 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1545 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1546 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1547 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1548 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1549 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1550 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1551 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1552 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1553 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1554 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1555 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1556 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1557 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1558 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1559 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1560 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1561 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1562 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1563 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1564 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1565 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1566 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1567 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1568 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1569 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1570 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1571 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1572 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1573 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1574 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1575 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1576 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1577 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1578 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1579 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1580 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1581 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1582 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1583 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1584 Small-Large unconnected 1.5862113 7.5 0.3935303
## 1585 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1586 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1587 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1588 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1589 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1590 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1591 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1592 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1593 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1594 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1595 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1596 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1597 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1598 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1599 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1600 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1601 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1602 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1603 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1604 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1605 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1606 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1607 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1608 Small-Large unconnected 1.4948352 8.5 0.6102781
## 1609 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1610 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1611 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1612 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1613 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1614 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1615 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1616 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1617 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1618 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1619 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1620 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1621 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1622 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1623 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1624 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1625 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1626 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1627 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1628 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1629 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1630 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1631 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1632 Small-Large unconnected 1.4254256 6.0 0.5077328
## 1633 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1634 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1635 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1636 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1637 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1638 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1639 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1640 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1641 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1642 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1643 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1644 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1645 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1646 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1647 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1648 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1649 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1650 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1651 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1652 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1653 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1654 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1655 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1656 Small-Large unconnected 1.1525871 4.5 0.7699053
## 1657 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1658 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1659 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1660 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1661 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1662 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1663 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1664 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1665 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1666 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1667 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1668 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1669 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1670 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1671 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1672 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1673 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1674 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1675 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1676 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1677 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1678 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1679 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1680 Small-Large unconnected 1.2474031 4.0 0.9374289
## 1681 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1682 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1683 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1684 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1685 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1686 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1687 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1688 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1689 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1690 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1691 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1692 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1693 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1694 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1695 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1696 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1697 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1698 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1699 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1700 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1701 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1702 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1703 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1704 Small-Large unconnected 0.7728167 3.5 0.7388350
## 1705 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1706 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1707 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1708 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1709 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1710 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1711 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1712 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1713 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1714 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1715 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1716 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1717 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1718 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1719 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1720 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1721 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1722 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1723 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1724 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1725 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1726 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1727 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1728 Small-Large unconnected 0.6460517 3.0 0.7497872
## 1729 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1730 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1731 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1732 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1733 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1734 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1735 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1736 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1737 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1738 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1739 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1740 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1741 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1742 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1743 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1744 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1745 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1746 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1747 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1748 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1749 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1750 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1751 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1752 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1753 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1754 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1755 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1756 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1757 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1758 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1759 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1760 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1761 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1762 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1763 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1764 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1765 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1766 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1767 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1768 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1769 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1770 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1771 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1772 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1773 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1774 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1775 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1776 Small-Large unconnected 1.8112725 8.5 0.5241108
## 1777 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1778 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1779 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1780 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1781 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1782 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1783 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1784 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1785 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1786 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1787 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1788 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1789 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1790 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1791 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1792 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1793 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1794 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1795 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1796 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1797 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1798 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1799 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1800 Small-Large unconnected 1.5778693 8.0 0.7006088
## 1801 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1802 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1803 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1804 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1805 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1806 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1807 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1808 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1809 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1810 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1811 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1812 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1813 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1814 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1815 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1816 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1817 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1818 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1819 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1820 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1821 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1822 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1823 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1824 Small-Large unconnected 1.7398154 7.0 0.4756098
## 1825 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1826 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1827 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1828 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1829 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1830 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1831 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1832 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1833 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1834 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1835 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1836 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1837 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1838 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1839 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1840 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1841 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1842 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1843 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1844 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1845 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1846 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1847 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1848 Small-Large unconnected 1.2519825 5.5 0.7460988
## 1849 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1850 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1851 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1852 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1853 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1854 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1855 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1856 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1857 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1858 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1859 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1860 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1861 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1862 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1863 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1864 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1865 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1866 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1867 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1868 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1869 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1870 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1871 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1872 Small-Large unconnected 1.4667712 5.5 0.9079875
## 1873 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1874 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1875 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1876 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1877 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1878 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1879 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1880 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1881 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1882 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1883 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1884 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1885 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1886 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1887 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1888 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1889 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1890 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1891 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1892 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1893 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1894 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1895 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1896 Small-Large unconnected 0.8928972 4.5 0.9027828
## 1897 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1898 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1899 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1900 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1901 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1902 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1903 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1904 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1905 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1906 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1907 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1908 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1909 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1910 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1911 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1912 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1913 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1914 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1915 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1916 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1917 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1918 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1919 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1920 Small-Large unconnected 0.6549539 4.5 0.9497693
## 1921 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1922 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1923 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1924 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1925 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1926 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1927 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1928 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1929 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1930 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1931 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1932 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1933 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1934 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1935 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1936 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1937 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1938 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1939 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1940 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1941 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1942 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1943 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1944 Small-Large unconnected 2.0784670 11.0 0.0000000
## 1945 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1946 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1947 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1948 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1949 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1950 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1951 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1952 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1953 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1954 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1955 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1956 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1957 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1958 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1959 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1960 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1961 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1962 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1963 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1964 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1965 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1966 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1967 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1968 Small-Large unconnected 1.4587022 7.0 0.4647482
## 1969 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1970 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1971 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1972 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1973 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1974 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1975 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1976 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1977 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1978 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1979 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1980 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1981 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1982 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1983 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1984 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1985 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1986 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1987 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1988 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1989 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1990 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1991 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1992 Small-Large unconnected 1.4635307 7.0 0.5222681
## 1993 Small-Large unconnected 1.4969088 6.0 0.6928848
## 1994 Small-Large unconnected 1.4969088 6.0 0.6928848
## 1995 Small-Large unconnected 1.4969088 6.0 0.6928848
## 1996 Small-Large unconnected 1.4969088 6.0 0.6928848
## 1997 Small-Large unconnected 1.4969088 6.0 0.6928848
## 1998 Small-Large unconnected 1.4969088 6.0 0.6928848
## 1999 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2000 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2001 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2002 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2003 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2004 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2005 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2006 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2007 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2008 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2009 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2010 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2011 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2012 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2013 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2014 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2015 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2016 Small-Large unconnected 1.4969088 6.0 0.6928848
## 2017 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2018 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2019 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2020 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2021 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2022 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2023 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2024 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2025 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2026 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2027 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2028 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2029 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2030 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2031 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2032 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2033 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2034 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2035 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2036 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2037 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2038 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2039 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2040 Small-Large unconnected 1.4098276 6.0 0.6760997
## 2041 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2042 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2043 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2044 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2045 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2046 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2047 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2048 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2049 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2050 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2051 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2052 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2053 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2054 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2055 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2056 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2057 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2058 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2059 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2060 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2061 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2062 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2063 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2064 Small-Large unconnected 0.8677885 4.0 0.8623853
## 2065 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2066 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2067 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2068 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2069 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2070 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2071 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2072 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2073 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2074 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2075 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2076 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2077 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2078 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2079 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2080 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2081 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2082 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2083 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2084 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2085 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2086 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2087 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2088 Small-Large unconnected 1.0349319 5.0 0.8940736
## 2089 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2090 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2091 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2092 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2093 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2094 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2095 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2096 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2097 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2098 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2099 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2100 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2101 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2102 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2103 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2104 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2105 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2106 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2107 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2108 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2109 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2110 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2111 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2112 Small-Large unconnected 0.8886913 5.5 0.8939828
## 2113 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2114 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2115 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2116 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2117 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2118 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2119 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2120 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2121 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2122 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2123 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2124 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2125 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2126 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2127 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2128 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2129 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2130 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2131 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2132 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2133 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2134 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2135 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2136 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2137 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2138 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2139 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2140 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2141 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2142 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2143 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2144 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2145 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2146 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2147 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2148 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2149 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2150 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2151 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2152 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2153 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2154 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2155 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2156 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2157 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2158 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2159 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2160 Small-Large unconnected 1.6928054 7.5 0.5989357
## 2161 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2162 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2163 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2164 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2165 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2166 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2167 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2168 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2169 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2170 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2171 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2172 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2173 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2174 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2175 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2176 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2177 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2178 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2179 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2180 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2181 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2182 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2183 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2184 Small-Large unconnected 1.3904874 5.5 0.2931267
## 2185 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2186 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2187 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2188 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2189 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2190 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2191 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2192 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2193 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2194 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2195 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2196 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2197 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2198 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2199 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2200 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2201 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2202 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2203 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2204 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2205 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2206 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2207 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2208 Small-Large unconnected 1.4161738 6.0 0.5734298
## 2209 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2210 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2211 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2212 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2213 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2214 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2215 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2216 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2217 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2218 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2219 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2220 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2221 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2222 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2223 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2224 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2225 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2226 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2227 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2228 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2229 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2230 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2231 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2232 Small-Large unconnected 1.1830432 4.5 0.5461783
## 2233 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2234 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2235 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2236 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2237 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2238 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2239 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2240 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2241 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2242 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2243 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2244 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2245 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2246 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2247 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2248 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2249 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2250 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2251 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2252 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2253 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2254 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2255 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2256 Small-Large unconnected 1.0779045 5.0 0.8424721
## 2257 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2258 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2259 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2260 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2261 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2262 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2263 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2264 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2265 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2266 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2267 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2268 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2269 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2270 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2271 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2272 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2273 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2274 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2275 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2276 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2277 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2278 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2279 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2280 Small-Large unconnected 1.1343318 5.0 0.9128705
## 2281 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2282 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2283 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2284 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2285 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2286 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2287 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2288 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2289 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2290 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2291 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2292 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2293 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2294 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2295 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2296 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2297 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2298 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2299 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2300 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2301 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2302 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2303 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2304 Small-Large unconnected 0.9541375 4.5 0.8634686
## 2305 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2306 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2307 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2308 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2309 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2310 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2311 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2312 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2313 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2314 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2315 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2316 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2317 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2318 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2319 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2320 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2321 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2322 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2323 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2324 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2325 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2326 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2327 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2328 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2329 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2330 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2331 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2332 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2333 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2334 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2335 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2336 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2337 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2338 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2339 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2340 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2341 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2342 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2343 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2344 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2345 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2346 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2347 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2348 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2349 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2350 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2351 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2352 Small-Large unconnected 1.5937474 7.5 0.3858672
## 2353 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2354 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2355 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2356 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2357 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2358 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2359 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2360 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2361 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2362 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2363 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2364 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2365 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2366 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2367 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2368 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2369 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2370 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2371 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2372 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2373 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2374 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2375 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2376 Small-Large unconnected 1.6035169 7.5 0.3980177
## 2377 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2378 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2379 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2380 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2381 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2382 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2383 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2384 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2385 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2386 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2387 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2388 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2389 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2390 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2391 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2392 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2393 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2394 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2395 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2396 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2397 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2398 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2399 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2400 Small-Large unconnected 1.5172828 6.5 0.6578032
## 2401 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2402 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2403 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2404 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2405 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2406 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2407 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2408 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2409 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2410 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2411 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2412 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2413 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2414 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2415 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2416 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2417 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2418 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2419 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2420 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2421 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2422 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2423 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2424 Small-Large unconnected 1.3203870 5.5 0.5871069
## 2425 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2426 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2427 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2428 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2429 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2430 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2431 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2432 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2433 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2434 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2435 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2436 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2437 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2438 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2439 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2440 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2441 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2442 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2443 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2444 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2445 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2446 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2447 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2448 Small-Large unconnected 0.9457610 4.0 0.8813489
## 2449 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2450 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2451 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2452 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2453 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2454 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2455 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2456 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2457 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2458 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2459 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2460 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2461 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2462 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2463 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2464 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2465 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2466 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2467 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2468 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2469 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2470 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2471 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2472 Small-Large unconnected 1.0476403 5.5 0.8832972
## 2473 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2474 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2475 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2476 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2477 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2478 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2479 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2480 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2481 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2482 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2483 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2484 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2485 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2486 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2487 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2488 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2489 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2490 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2491 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2492 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2493 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2494 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2495 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2496 Small-Large unconnected 0.8264735 4.5 0.9161354
## 2497 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2498 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2499 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2500 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2501 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2502 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2503 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2504 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2505 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2506 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2507 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2508 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2509 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2510 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2511 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2512 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2513 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2514 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2515 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2516 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2517 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2518 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2519 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2520 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2521 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2522 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2523 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2524 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2525 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2526 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2527 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2528 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2529 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2530 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2531 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2532 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2533 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2534 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2535 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2536 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2537 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2538 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2539 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2540 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2541 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2542 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2543 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2544 Small-Large unconnected 1.4908950 6.5 0.4258033
## 2545 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2546 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2547 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2548 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2549 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2550 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2551 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2552 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2553 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2554 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2555 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2556 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2557 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2558 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2559 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2560 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2561 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2562 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2563 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2564 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2565 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2566 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2567 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2568 Small-Large unconnected 1.4369842 7.0 0.5152690
## 2569 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2570 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2571 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2572 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2573 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2574 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2575 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2576 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2577 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2578 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2579 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2580 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2581 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2582 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2583 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2584 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2585 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2586 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2587 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2588 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2589 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2590 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2591 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2592 Small-Large unconnected 1.1590750 5.0 0.3094595
## 2593 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2594 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2595 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2596 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2597 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2598 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2599 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2600 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2601 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2602 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2603 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2604 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2605 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2606 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2607 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2608 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2609 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2610 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2611 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2612 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2613 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2614 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2615 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2616 Small-Large unconnected 1.1787010 5.0 0.5881557
## 2617 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2618 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2619 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2620 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2621 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2622 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2623 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2624 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2625 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2626 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2627 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2628 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2629 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2630 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2631 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2632 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2633 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2634 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2635 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2636 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2637 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2638 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2639 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2640 Small-Large unconnected 0.9245130 3.5 0.8128693
## 2641 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2642 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2643 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2644 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2645 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2646 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2647 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2648 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2649 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2650 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2651 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2652 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2653 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2654 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2655 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2656 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2657 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2658 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2659 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2660 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2661 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2662 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2663 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2664 Small-Large unconnected 1.2497340 4.5 0.8109840
## 2665 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2666 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2667 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2668 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2669 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2670 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2671 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2672 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2673 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2674 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2675 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2676 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2677 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2678 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2679 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2680 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2681 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2682 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2683 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2684 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2685 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2686 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2687 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2688 Small-Large unconnected 0.8774006 3.5 0.7224848
## 2689 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2690 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2691 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2692 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2693 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2694 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2695 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2696 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2697 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2698 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2699 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2700 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2701 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2702 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2703 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2704 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2705 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2706 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2707 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2708 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2709 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2710 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2711 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2712 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2713 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2714 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2715 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2716 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2717 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2718 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2719 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2720 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2721 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2722 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2723 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2724 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2725 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2726 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2727 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2728 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2729 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2730 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2731 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2732 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2733 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2734 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2735 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2736 Small-Large unconnected 1.7159561 7.5 0.6949506
## 2737 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2738 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2739 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2740 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2741 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2742 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2743 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2744 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2745 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2746 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2747 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2748 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2749 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2750 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2751 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2752 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2753 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2754 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2755 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2756 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2757 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2758 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2759 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2760 Small-Large unconnected 1.5200182 6.5 0.4408897
## 2761 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2762 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2763 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2764 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2765 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2766 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2767 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2768 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2769 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2770 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2771 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2772 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2773 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2774 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2775 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2776 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2777 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2778 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2779 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2780 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2781 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2782 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2783 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2784 Small-Large unconnected 1.4734648 6.0 0.5394322
## 2785 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2786 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2787 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2788 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2789 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2790 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2791 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2792 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2793 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2794 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2795 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2796 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2797 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2798 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2799 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2800 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2801 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2802 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2803 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2804 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2805 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2806 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2807 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2808 Small-Large unconnected 1.2780964 6.0 0.5398773
## 2809 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2810 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2811 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2812 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2813 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2814 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2815 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2816 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2817 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2818 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2819 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2820 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2821 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2822 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2823 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2824 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2825 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2826 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2827 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2828 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2829 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2830 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2831 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2832 Small-Large unconnected 1.1438811 5.0 0.8833879
## 2833 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2834 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2835 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2836 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2837 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2838 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2839 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2840 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2841 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2842 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2843 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2844 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2845 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2846 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2847 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2848 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2849 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2850 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2851 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2852 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2853 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2854 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2855 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2856 Small-Large unconnected 1.3698145 5.5 0.9027828
## 2857 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2858 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2859 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2860 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2861 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2862 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2863 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2864 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2865 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2866 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2867 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2868 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2869 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2870 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2871 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2872 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2873 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2874 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2875 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2876 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2877 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2878 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2879 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2880 Small-Large unconnected 0.8863028 5.0 0.9009702
## 2881 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2882 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2883 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2884 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2885 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2886 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2887 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2888 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2889 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2890 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2891 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2892 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2893 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2894 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2895 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2896 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2897 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2898 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2899 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2900 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2901 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2902 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2903 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2904 Small-Large unconnected 2.0784670 11.0 0.0000000
## 2905 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2906 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2907 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2908 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2909 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2910 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2911 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2912 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2913 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2914 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2915 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2916 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2917 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2918 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2919 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2920 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2921 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2922 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2923 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2924 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2925 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2926 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2927 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2928 Small-Large unconnected 1.4093629 7.5 0.3571855
## 2929 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2930 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2931 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2932 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2933 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2934 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2935 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2936 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2937 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2938 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2939 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2940 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2941 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2942 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2943 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2944 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2945 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2946 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2947 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2948 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2949 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2950 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2951 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2952 Small-Large unconnected 1.5566020 8.0 0.4330945
## 2953 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2954 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2955 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2956 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2957 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2958 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2959 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2960 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2961 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2962 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2963 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2964 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2965 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2966 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2967 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2968 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2969 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2970 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2971 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2972 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2973 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2974 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2975 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2976 Small-Large unconnected 1.3271205 5.0 0.7095691
## 2977 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2978 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2979 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2980 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2981 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2982 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2983 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2984 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2985 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2986 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2987 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2988 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2989 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2990 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2991 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2992 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2993 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2994 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2995 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2996 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2997 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2998 Small-Large unconnected 1.4700682 6.0 0.5603006
## 2999 Small-Large unconnected 1.4700682 6.0 0.5603006
## 3000 Small-Large unconnected 1.4700682 6.0 0.5603006
## 3001 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3002 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3003 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3004 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3005 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3006 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3007 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3008 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3009 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3010 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3011 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3012 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3013 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3014 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3015 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3016 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3017 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3018 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3019 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3020 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3021 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3022 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3023 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3024 Small-Large unconnected 1.0940609 4.5 0.8165592
## 3025 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3026 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3027 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3028 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3029 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3030 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3031 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3032 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3033 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3034 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3035 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3036 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3037 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3038 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3039 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3040 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3041 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3042 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3043 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3044 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3045 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3046 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3047 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3048 Small-Large unconnected 0.8851120 4.5 0.9186702
## 3049 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3050 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3051 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3052 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3053 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3054 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3055 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3056 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3057 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3058 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3059 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3060 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3061 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3062 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3063 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3064 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3065 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3066 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3067 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3068 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3069 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3070 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3071 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3072 Small-Large unconnected 1.3912750 7.0 0.8836783
## 3073 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3074 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3075 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3076 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3077 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3078 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3079 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3080 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3081 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3082 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3083 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3084 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3085 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3086 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3087 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3088 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3089 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3090 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3091 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3092 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3093 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3094 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3095 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3096 Small-Large unconnected 2.0784670 11.0 0.0000000
## 3097 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3098 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3099 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3100 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3101 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3102 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3103 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3104 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3105 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3106 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3107 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3108 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3109 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3110 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3111 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3112 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3113 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3114 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3115 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3116 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3117 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3118 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3119 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3120 Small-Large unconnected 1.6434662 8.0 0.6412607
## 3121 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3122 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3123 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3124 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3125 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3126 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3127 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3128 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3129 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3130 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3131 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3132 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3133 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3134 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3135 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3136 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3137 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3138 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3139 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3140 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3141 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3142 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3143 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3144 Small-Large unconnected 1.4835587 6.5 0.3623978
## 3145 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3146 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3147 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3148 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3149 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3150 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3151 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3152 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3153 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3154 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3155 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3156 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3157 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3158 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3159 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3160 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3161 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3162 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3163 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3164 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3165 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3166 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3167 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3168 Small-Large unconnected 1.2463855 5.0 0.7793072
## 3169 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3170 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3171 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3172 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3173 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3174 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3175 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3176 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3177 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3178 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3179 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3180 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3181 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3182 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3183 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3184 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3185 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3186 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3187 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3188 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3189 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3190 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3191 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3192 Small-Large unconnected 1.2432838 4.5 0.6892984
## 3193 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3194 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3195 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3196 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3197 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3198 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3199 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3200 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3201 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3202 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3203 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3204 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3205 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3206 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3207 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3208 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3209 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3210 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3211 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3212 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3213 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3214 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3215 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3216 Small-Large unconnected 1.3041770 5.5 0.8280669
## 3217 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3218 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3219 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3220 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3221 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3222 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3223 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3224 Small-Large unconnected 0.9845120 4.5 0.8706428
## 3225 Small-Large unconnected 0.9845120 4.5 0.8706428
## bray_curtis beta_spatial_turnover beta_nestedness beta_total
## 1 0.0000000 0.0000000 0.00000000 0.00000000
## 2 0.0000000 0.0000000 0.00000000 0.00000000
## 3 0.0000000 0.0000000 0.00000000 0.00000000
## 4 0.0000000 0.0000000 0.00000000 0.00000000
## 5 0.0000000 0.0000000 0.00000000 0.00000000
## 6 0.0000000 0.0000000 0.00000000 0.00000000
## 7 0.0000000 0.0000000 0.00000000 0.00000000
## 8 0.0000000 0.0000000 0.00000000 0.00000000
## 9 0.0000000 0.0000000 0.00000000 0.00000000
## 10 0.0000000 0.0000000 0.00000000 0.00000000
## 11 0.0000000 0.0000000 0.00000000 0.00000000
## 12 0.0000000 0.0000000 0.00000000 0.00000000
## 13 0.0000000 0.0000000 0.00000000 0.00000000
## 14 0.0000000 0.0000000 0.00000000 0.00000000
## 15 0.0000000 0.0000000 0.00000000 0.00000000
## 16 0.0000000 0.0000000 0.00000000 0.00000000
## 17 0.0000000 0.0000000 0.00000000 0.00000000
## 18 0.0000000 0.0000000 0.00000000 0.00000000
## 19 0.0000000 0.0000000 0.00000000 0.00000000
## 20 0.0000000 0.0000000 0.00000000 0.00000000
## 21 0.0000000 0.0000000 0.00000000 0.00000000
## 22 0.0000000 0.0000000 0.00000000 0.00000000
## 23 0.0000000 0.0000000 0.00000000 0.00000000
## 24 0.0000000 0.0000000 0.00000000 0.00000000
## 25 0.2343643 0.1428571 0.05714286 0.20000000
## 26 0.2343643 0.1428571 0.05714286 0.20000000
## 27 0.2343643 0.1428571 0.05714286 0.20000000
## 28 0.2343643 0.1428571 0.05714286 0.20000000
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## 482 0.3792106 0.2857143 0.00000000 0.28571429
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## 885 0.3401808 0.1428571 0.05714286 0.20000000
## 886 0.3401808 0.1428571 0.05714286 0.20000000
## 887 0.3401808 0.1428571 0.05714286 0.20000000
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## 1058 0.4418719 0.0000000 0.45454545 0.45454545
## 1059 0.4418719 0.0000000 0.45454545 0.45454545
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## 1061 0.4418719 0.0000000 0.45454545 0.45454545
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## 1078 0.4418719 0.0000000 0.45454545 0.45454545
## 1079 0.4418719 0.0000000 0.45454545 0.45454545
## 1080 0.4418719 0.0000000 0.45454545 0.45454545
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## 1228 0.3505514 0.1666667 0.11904762 0.28571429
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## 1242 0.3505514 0.1666667 0.11904762 0.28571429
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## 1245 0.3505514 0.1666667 0.11904762 0.28571429
## 1246 0.3505514 0.1666667 0.11904762 0.28571429
## 1247 0.3505514 0.1666667 0.11904762 0.28571429
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## 1280 0.7404939 0.0000000 0.45454545 0.45454545
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## 1283 0.7404939 0.0000000 0.45454545 0.45454545
## 1284 0.7404939 0.0000000 0.45454545 0.45454545
## 1285 0.7404939 0.0000000 0.45454545 0.45454545
## 1286 0.7404939 0.0000000 0.45454545 0.45454545
## 1287 0.7404939 0.0000000 0.45454545 0.45454545
## 1288 0.7404939 0.0000000 0.45454545 0.45454545
## 1289 0.7404939 0.0000000 0.45454545 0.45454545
## 1290 0.7404939 0.0000000 0.45454545 0.45454545
## 1291 0.7404939 0.0000000 0.45454545 0.45454545
## 1292 0.7404939 0.0000000 0.45454545 0.45454545
## 1293 0.7404939 0.0000000 0.45454545 0.45454545
## 1294 0.7404939 0.0000000 0.45454545 0.45454545
## 1295 0.7404939 0.0000000 0.45454545 0.45454545
## 1296 0.7404939 0.0000000 0.45454545 0.45454545
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## 1378 0.3469772 0.1250000 0.05147059 0.17647059
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## 1383 0.3469772 0.1250000 0.05147059 0.17647059
## 1384 0.3469772 0.1250000 0.05147059 0.17647059
## 1385 0.3469772 0.1250000 0.05147059 0.17647059
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## 1387 0.3469772 0.1250000 0.05147059 0.17647059
## 1388 0.3469772 0.1250000 0.05147059 0.17647059
## 1389 0.3469772 0.1250000 0.05147059 0.17647059
## 1390 0.3469772 0.1250000 0.05147059 0.17647059
## 1391 0.3469772 0.1250000 0.05147059 0.17647059
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## 1421 0.3385088 0.0000000 0.20000000 0.20000000
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## 1458 0.5940439 0.3333333 0.26666667 0.60000000
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## 1460 0.5940439 0.3333333 0.26666667 0.60000000
## 1461 0.5940439 0.3333333 0.26666667 0.60000000
## 1462 0.5940439 0.3333333 0.26666667 0.60000000
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## 1479 0.8289043 0.3333333 0.22222222 0.55555556
## 1480 0.8289043 0.3333333 0.22222222 0.55555556
## 1481 0.8289043 0.3333333 0.22222222 0.55555556
## 1482 0.8289043 0.3333333 0.22222222 0.55555556
## 1483 0.8289043 0.3333333 0.22222222 0.55555556
## 1484 0.8289043 0.3333333 0.22222222 0.55555556
## 1485 0.8289043 0.3333333 0.22222222 0.55555556
## 1486 0.8289043 0.3333333 0.22222222 0.55555556
## 1487 0.8289043 0.3333333 0.22222222 0.55555556
## 1488 0.8289043 0.3333333 0.22222222 0.55555556
## 1489 0.7909868 0.0000000 0.77777778 0.77777778
## 1490 0.7909868 0.0000000 0.77777778 0.77777778
## 1491 0.7909868 0.0000000 0.77777778 0.77777778
## 1492 0.7909868 0.0000000 0.77777778 0.77777778
## 1493 0.7909868 0.0000000 0.77777778 0.77777778
## 1494 0.7909868 0.0000000 0.77777778 0.77777778
## 1495 0.7909868 0.0000000 0.77777778 0.77777778
## 1496 0.7909868 0.0000000 0.77777778 0.77777778
## 1497 0.7909868 0.0000000 0.77777778 0.77777778
## 1498 0.7909868 0.0000000 0.77777778 0.77777778
## 1499 0.7909868 0.0000000 0.77777778 0.77777778
## 1500 0.7909868 0.0000000 0.77777778 0.77777778
## 1501 0.7909868 0.0000000 0.77777778 0.77777778
## 1502 0.7909868 0.0000000 0.77777778 0.77777778
## 1503 0.7909868 0.0000000 0.77777778 0.77777778
## 1504 0.7909868 0.0000000 0.77777778 0.77777778
## 1505 0.7909868 0.0000000 0.77777778 0.77777778
## 1506 0.7909868 0.0000000 0.77777778 0.77777778
## 1507 0.7909868 0.0000000 0.77777778 0.77777778
## 1508 0.7909868 0.0000000 0.77777778 0.77777778
## 1509 0.7909868 0.0000000 0.77777778 0.77777778
## 1510 0.7909868 0.0000000 0.77777778 0.77777778
## 1511 0.7909868 0.0000000 0.77777778 0.77777778
## 1512 0.7909868 0.0000000 0.77777778 0.77777778
## 1513 0.9186497 0.0000000 0.75000000 0.75000000
## 1514 0.9186497 0.0000000 0.75000000 0.75000000
## 1515 0.9186497 0.0000000 0.75000000 0.75000000
## 1516 0.9186497 0.0000000 0.75000000 0.75000000
## 1517 0.9186497 0.0000000 0.75000000 0.75000000
## 1518 0.9186497 0.0000000 0.75000000 0.75000000
## 1519 0.9186497 0.0000000 0.75000000 0.75000000
## 1520 0.9186497 0.0000000 0.75000000 0.75000000
## 1521 0.9186497 0.0000000 0.75000000 0.75000000
## 1522 0.9186497 0.0000000 0.75000000 0.75000000
## 1523 0.9186497 0.0000000 0.75000000 0.75000000
## 1524 0.9186497 0.0000000 0.75000000 0.75000000
## 1525 0.9186497 0.0000000 0.75000000 0.75000000
## 1526 0.9186497 0.0000000 0.75000000 0.75000000
## 1527 0.9186497 0.0000000 0.75000000 0.75000000
## 1528 0.9186497 0.0000000 0.75000000 0.75000000
## 1529 0.9186497 0.0000000 0.75000000 0.75000000
## 1530 0.9186497 0.0000000 0.75000000 0.75000000
## 1531 0.9186497 0.0000000 0.75000000 0.75000000
## 1532 0.9186497 0.0000000 0.75000000 0.75000000
## 1533 0.9186497 0.0000000 0.75000000 0.75000000
## 1534 0.9186497 0.0000000 0.75000000 0.75000000
## 1535 0.9186497 0.0000000 0.75000000 0.75000000
## 1536 0.9186497 0.0000000 0.75000000 0.75000000
## 1537 0.0000000 0.0000000 0.00000000 0.00000000
## 1538 0.0000000 0.0000000 0.00000000 0.00000000
## 1539 0.0000000 0.0000000 0.00000000 0.00000000
## 1540 0.0000000 0.0000000 0.00000000 0.00000000
## 1541 0.0000000 0.0000000 0.00000000 0.00000000
## 1542 0.0000000 0.0000000 0.00000000 0.00000000
## 1543 0.0000000 0.0000000 0.00000000 0.00000000
## 1544 0.0000000 0.0000000 0.00000000 0.00000000
## 1545 0.0000000 0.0000000 0.00000000 0.00000000
## 1546 0.0000000 0.0000000 0.00000000 0.00000000
## 1547 0.0000000 0.0000000 0.00000000 0.00000000
## 1548 0.0000000 0.0000000 0.00000000 0.00000000
## 1549 0.0000000 0.0000000 0.00000000 0.00000000
## 1550 0.0000000 0.0000000 0.00000000 0.00000000
## 1551 0.0000000 0.0000000 0.00000000 0.00000000
## 1552 0.0000000 0.0000000 0.00000000 0.00000000
## 1553 0.0000000 0.0000000 0.00000000 0.00000000
## 1554 0.0000000 0.0000000 0.00000000 0.00000000
## 1555 0.0000000 0.0000000 0.00000000 0.00000000
## 1556 0.0000000 0.0000000 0.00000000 0.00000000
## 1557 0.0000000 0.0000000 0.00000000 0.00000000
## 1558 0.0000000 0.0000000 0.00000000 0.00000000
## 1559 0.0000000 0.0000000 0.00000000 0.00000000
## 1560 0.0000000 0.0000000 0.00000000 0.00000000
## 1561 0.2449659 0.1428571 0.05714286 0.20000000
## 1562 0.2449659 0.1428571 0.05714286 0.20000000
## 1563 0.2449659 0.1428571 0.05714286 0.20000000
## 1564 0.2449659 0.1428571 0.05714286 0.20000000
## 1565 0.2449659 0.1428571 0.05714286 0.20000000
## 1566 0.2449659 0.1428571 0.05714286 0.20000000
## 1567 0.2449659 0.1428571 0.05714286 0.20000000
## 1568 0.2449659 0.1428571 0.05714286 0.20000000
## 1569 0.2449659 0.1428571 0.05714286 0.20000000
## 1570 0.2449659 0.1428571 0.05714286 0.20000000
## 1571 0.2449659 0.1428571 0.05714286 0.20000000
## 1572 0.2449659 0.1428571 0.05714286 0.20000000
## 1573 0.2449659 0.1428571 0.05714286 0.20000000
## 1574 0.2449659 0.1428571 0.05714286 0.20000000
## 1575 0.2449659 0.1428571 0.05714286 0.20000000
## 1576 0.2449659 0.1428571 0.05714286 0.20000000
## 1577 0.2449659 0.1428571 0.05714286 0.20000000
## 1578 0.2449659 0.1428571 0.05714286 0.20000000
## 1579 0.2449659 0.1428571 0.05714286 0.20000000
## 1580 0.2449659 0.1428571 0.05714286 0.20000000
## 1581 0.2449659 0.1428571 0.05714286 0.20000000
## 1582 0.2449659 0.1428571 0.05714286 0.20000000
## 1583 0.2449659 0.1428571 0.05714286 0.20000000
## 1584 0.2449659 0.1428571 0.05714286 0.20000000
## 1585 0.4391368 0.1250000 0.05147059 0.17647059
## 1586 0.4391368 0.1250000 0.05147059 0.17647059
## 1587 0.4391368 0.1250000 0.05147059 0.17647059
## 1588 0.4391368 0.1250000 0.05147059 0.17647059
## 1589 0.4391368 0.1250000 0.05147059 0.17647059
## 1590 0.4391368 0.1250000 0.05147059 0.17647059
## 1591 0.4391368 0.1250000 0.05147059 0.17647059
## 1592 0.4391368 0.1250000 0.05147059 0.17647059
## 1593 0.4391368 0.1250000 0.05147059 0.17647059
## 1594 0.4391368 0.1250000 0.05147059 0.17647059
## 1595 0.4391368 0.1250000 0.05147059 0.17647059
## 1596 0.4391368 0.1250000 0.05147059 0.17647059
## 1597 0.4391368 0.1250000 0.05147059 0.17647059
## 1598 0.4391368 0.1250000 0.05147059 0.17647059
## 1599 0.4391368 0.1250000 0.05147059 0.17647059
## 1600 0.4391368 0.1250000 0.05147059 0.17647059
## 1601 0.4391368 0.1250000 0.05147059 0.17647059
## 1602 0.4391368 0.1250000 0.05147059 0.17647059
## 1603 0.4391368 0.1250000 0.05147059 0.17647059
## 1604 0.4391368 0.1250000 0.05147059 0.17647059
## 1605 0.4391368 0.1250000 0.05147059 0.17647059
## 1606 0.4391368 0.1250000 0.05147059 0.17647059
## 1607 0.4391368 0.1250000 0.05147059 0.17647059
## 1608 0.4391368 0.1250000 0.05147059 0.17647059
## 1609 0.3402426 0.1666667 0.00000000 0.16666667
## 1610 0.3402426 0.1666667 0.00000000 0.16666667
## 1611 0.3402426 0.1666667 0.00000000 0.16666667
## 1612 0.3402426 0.1666667 0.00000000 0.16666667
## 1613 0.3402426 0.1666667 0.00000000 0.16666667
## 1614 0.3402426 0.1666667 0.00000000 0.16666667
## 1615 0.3402426 0.1666667 0.00000000 0.16666667
## 1616 0.3402426 0.1666667 0.00000000 0.16666667
## 1617 0.3402426 0.1666667 0.00000000 0.16666667
## 1618 0.3402426 0.1666667 0.00000000 0.16666667
## 1619 0.3402426 0.1666667 0.00000000 0.16666667
## 1620 0.3402426 0.1666667 0.00000000 0.16666667
## 1621 0.3402426 0.1666667 0.00000000 0.16666667
## 1622 0.3402426 0.1666667 0.00000000 0.16666667
## 1623 0.3402426 0.1666667 0.00000000 0.16666667
## 1624 0.3402426 0.1666667 0.00000000 0.16666667
## 1625 0.3402426 0.1666667 0.00000000 0.16666667
## 1626 0.3402426 0.1666667 0.00000000 0.16666667
## 1627 0.3402426 0.1666667 0.00000000 0.16666667
## 1628 0.3402426 0.1666667 0.00000000 0.16666667
## 1629 0.3402426 0.1666667 0.00000000 0.16666667
## 1630 0.3402426 0.1666667 0.00000000 0.16666667
## 1631 0.3402426 0.1666667 0.00000000 0.16666667
## 1632 0.3402426 0.1666667 0.00000000 0.16666667
## 1633 0.6258911 0.6666667 0.11111111 0.77777778
## 1634 0.6258911 0.6666667 0.11111111 0.77777778
## 1635 0.6258911 0.6666667 0.11111111 0.77777778
## 1636 0.6258911 0.6666667 0.11111111 0.77777778
## 1637 0.6258911 0.6666667 0.11111111 0.77777778
## 1638 0.6258911 0.6666667 0.11111111 0.77777778
## 1639 0.6258911 0.6666667 0.11111111 0.77777778
## 1640 0.6258911 0.6666667 0.11111111 0.77777778
## 1641 0.6258911 0.6666667 0.11111111 0.77777778
## 1642 0.6258911 0.6666667 0.11111111 0.77777778
## 1643 0.6258911 0.6666667 0.11111111 0.77777778
## 1644 0.6258911 0.6666667 0.11111111 0.77777778
## 1645 0.6258911 0.6666667 0.11111111 0.77777778
## 1646 0.6258911 0.6666667 0.11111111 0.77777778
## 1647 0.6258911 0.6666667 0.11111111 0.77777778
## 1648 0.6258911 0.6666667 0.11111111 0.77777778
## 1649 0.6258911 0.6666667 0.11111111 0.77777778
## 1650 0.6258911 0.6666667 0.11111111 0.77777778
## 1651 0.6258911 0.6666667 0.11111111 0.77777778
## 1652 0.6258911 0.6666667 0.11111111 0.77777778
## 1653 0.6258911 0.6666667 0.11111111 0.77777778
## 1654 0.6258911 0.6666667 0.11111111 0.77777778
## 1655 0.6258911 0.6666667 0.11111111 0.77777778
## 1656 0.6258911 0.6666667 0.11111111 0.77777778
## 1657 0.8822270 0.6666667 0.08333333 0.75000000
## 1658 0.8822270 0.6666667 0.08333333 0.75000000
## 1659 0.8822270 0.6666667 0.08333333 0.75000000
## 1660 0.8822270 0.6666667 0.08333333 0.75000000
## 1661 0.8822270 0.6666667 0.08333333 0.75000000
## 1662 0.8822270 0.6666667 0.08333333 0.75000000
## 1663 0.8822270 0.6666667 0.08333333 0.75000000
## 1664 0.8822270 0.6666667 0.08333333 0.75000000
## 1665 0.8822270 0.6666667 0.08333333 0.75000000
## 1666 0.8822270 0.6666667 0.08333333 0.75000000
## 1667 0.8822270 0.6666667 0.08333333 0.75000000
## 1668 0.8822270 0.6666667 0.08333333 0.75000000
## 1669 0.8822270 0.6666667 0.08333333 0.75000000
## 1670 0.8822270 0.6666667 0.08333333 0.75000000
## 1671 0.8822270 0.6666667 0.08333333 0.75000000
## 1672 0.8822270 0.6666667 0.08333333 0.75000000
## 1673 0.8822270 0.6666667 0.08333333 0.75000000
## 1674 0.8822270 0.6666667 0.08333333 0.75000000
## 1675 0.8822270 0.6666667 0.08333333 0.75000000
## 1676 0.8822270 0.6666667 0.08333333 0.75000000
## 1677 0.8822270 0.6666667 0.08333333 0.75000000
## 1678 0.8822270 0.6666667 0.08333333 0.75000000
## 1679 0.8822270 0.6666667 0.08333333 0.75000000
## 1680 0.8822270 0.6666667 0.08333333 0.75000000
## 1681 0.5858353 0.0000000 0.71428571 0.71428571
## 1682 0.5858353 0.0000000 0.71428571 0.71428571
## 1683 0.5858353 0.0000000 0.71428571 0.71428571
## 1684 0.5858353 0.0000000 0.71428571 0.71428571
## 1685 0.5858353 0.0000000 0.71428571 0.71428571
## 1686 0.5858353 0.0000000 0.71428571 0.71428571
## 1687 0.5858353 0.0000000 0.71428571 0.71428571
## 1688 0.5858353 0.0000000 0.71428571 0.71428571
## 1689 0.5858353 0.0000000 0.71428571 0.71428571
## 1690 0.5858353 0.0000000 0.71428571 0.71428571
## 1691 0.5858353 0.0000000 0.71428571 0.71428571
## 1692 0.5858353 0.0000000 0.71428571 0.71428571
## 1693 0.5858353 0.0000000 0.71428571 0.71428571
## 1694 0.5858353 0.0000000 0.71428571 0.71428571
## 1695 0.5858353 0.0000000 0.71428571 0.71428571
## 1696 0.5858353 0.0000000 0.71428571 0.71428571
## 1697 0.5858353 0.0000000 0.71428571 0.71428571
## 1698 0.5858353 0.0000000 0.71428571 0.71428571
## 1699 0.5858353 0.0000000 0.71428571 0.71428571
## 1700 0.5858353 0.0000000 0.71428571 0.71428571
## 1701 0.5858353 0.0000000 0.71428571 0.71428571
## 1702 0.5858353 0.0000000 0.71428571 0.71428571
## 1703 0.5858353 0.0000000 0.71428571 0.71428571
## 1704 0.5858353 0.0000000 0.71428571 0.71428571
## 1705 0.5997277 0.0000000 0.66666667 0.66666667
## 1706 0.5997277 0.0000000 0.66666667 0.66666667
## 1707 0.5997277 0.0000000 0.66666667 0.66666667
## 1708 0.5997277 0.0000000 0.66666667 0.66666667
## 1709 0.5997277 0.0000000 0.66666667 0.66666667
## 1710 0.5997277 0.0000000 0.66666667 0.66666667
## 1711 0.5997277 0.0000000 0.66666667 0.66666667
## 1712 0.5997277 0.0000000 0.66666667 0.66666667
## 1713 0.5997277 0.0000000 0.66666667 0.66666667
## 1714 0.5997277 0.0000000 0.66666667 0.66666667
## 1715 0.5997277 0.0000000 0.66666667 0.66666667
## 1716 0.5997277 0.0000000 0.66666667 0.66666667
## 1717 0.5997277 0.0000000 0.66666667 0.66666667
## 1718 0.5997277 0.0000000 0.66666667 0.66666667
## 1719 0.5997277 0.0000000 0.66666667 0.66666667
## 1720 0.5997277 0.0000000 0.66666667 0.66666667
## 1721 0.5997277 0.0000000 0.66666667 0.66666667
## 1722 0.5997277 0.0000000 0.66666667 0.66666667
## 1723 0.5997277 0.0000000 0.66666667 0.66666667
## 1724 0.5997277 0.0000000 0.66666667 0.66666667
## 1725 0.5997277 0.0000000 0.66666667 0.66666667
## 1726 0.5997277 0.0000000 0.66666667 0.66666667
## 1727 0.5997277 0.0000000 0.66666667 0.66666667
## 1728 0.5997277 0.0000000 0.66666667 0.66666667
## 1729 0.0000000 0.0000000 0.00000000 0.00000000
## 1730 0.0000000 0.0000000 0.00000000 0.00000000
## 1731 0.0000000 0.0000000 0.00000000 0.00000000
## 1732 0.0000000 0.0000000 0.00000000 0.00000000
## 1733 0.0000000 0.0000000 0.00000000 0.00000000
## 1734 0.0000000 0.0000000 0.00000000 0.00000000
## 1735 0.0000000 0.0000000 0.00000000 0.00000000
## 1736 0.0000000 0.0000000 0.00000000 0.00000000
## 1737 0.0000000 0.0000000 0.00000000 0.00000000
## 1738 0.0000000 0.0000000 0.00000000 0.00000000
## 1739 0.0000000 0.0000000 0.00000000 0.00000000
## 1740 0.0000000 0.0000000 0.00000000 0.00000000
## 1741 0.0000000 0.0000000 0.00000000 0.00000000
## 1742 0.0000000 0.0000000 0.00000000 0.00000000
## 1743 0.0000000 0.0000000 0.00000000 0.00000000
## 1744 0.0000000 0.0000000 0.00000000 0.00000000
## 1745 0.0000000 0.0000000 0.00000000 0.00000000
## 1746 0.0000000 0.0000000 0.00000000 0.00000000
## 1747 0.0000000 0.0000000 0.00000000 0.00000000
## 1748 0.0000000 0.0000000 0.00000000 0.00000000
## 1749 0.0000000 0.0000000 0.00000000 0.00000000
## 1750 0.0000000 0.0000000 0.00000000 0.00000000
## 1751 0.0000000 0.0000000 0.00000000 0.00000000
## 1752 0.0000000 0.0000000 0.00000000 0.00000000
## 1753 0.3551153 0.0000000 0.05882353 0.05882353
## 1754 0.3551153 0.0000000 0.05882353 0.05882353
## 1755 0.3551153 0.0000000 0.05882353 0.05882353
## 1756 0.3551153 0.0000000 0.05882353 0.05882353
## 1757 0.3551153 0.0000000 0.05882353 0.05882353
## 1758 0.3551153 0.0000000 0.05882353 0.05882353
## 1759 0.3551153 0.0000000 0.05882353 0.05882353
## 1760 0.3551153 0.0000000 0.05882353 0.05882353
## 1761 0.3551153 0.0000000 0.05882353 0.05882353
## 1762 0.3551153 0.0000000 0.05882353 0.05882353
## 1763 0.3551153 0.0000000 0.05882353 0.05882353
## 1764 0.3551153 0.0000000 0.05882353 0.05882353
## 1765 0.3551153 0.0000000 0.05882353 0.05882353
## 1766 0.3551153 0.0000000 0.05882353 0.05882353
## 1767 0.3551153 0.0000000 0.05882353 0.05882353
## 1768 0.3551153 0.0000000 0.05882353 0.05882353
## 1769 0.3551153 0.0000000 0.05882353 0.05882353
## 1770 0.3551153 0.0000000 0.05882353 0.05882353
## 1771 0.3551153 0.0000000 0.05882353 0.05882353
## 1772 0.3551153 0.0000000 0.05882353 0.05882353
## 1773 0.3551153 0.0000000 0.05882353 0.05882353
## 1774 0.3551153 0.0000000 0.05882353 0.05882353
## 1775 0.3551153 0.0000000 0.05882353 0.05882353
## 1776 0.3551153 0.0000000 0.05882353 0.05882353
## 1777 0.5391824 0.1428571 0.10714286 0.25000000
## 1778 0.5391824 0.1428571 0.10714286 0.25000000
## 1779 0.5391824 0.1428571 0.10714286 0.25000000
## 1780 0.5391824 0.1428571 0.10714286 0.25000000
## 1781 0.5391824 0.1428571 0.10714286 0.25000000
## 1782 0.5391824 0.1428571 0.10714286 0.25000000
## 1783 0.5391824 0.1428571 0.10714286 0.25000000
## 1784 0.5391824 0.1428571 0.10714286 0.25000000
## 1785 0.5391824 0.1428571 0.10714286 0.25000000
## 1786 0.5391824 0.1428571 0.10714286 0.25000000
## 1787 0.5391824 0.1428571 0.10714286 0.25000000
## 1788 0.5391824 0.1428571 0.10714286 0.25000000
## 1789 0.5391824 0.1428571 0.10714286 0.25000000
## 1790 0.5391824 0.1428571 0.10714286 0.25000000
## 1791 0.5391824 0.1428571 0.10714286 0.25000000
## 1792 0.5391824 0.1428571 0.10714286 0.25000000
## 1793 0.5391824 0.1428571 0.10714286 0.25000000
## 1794 0.5391824 0.1428571 0.10714286 0.25000000
## 1795 0.5391824 0.1428571 0.10714286 0.25000000
## 1796 0.5391824 0.1428571 0.10714286 0.25000000
## 1797 0.5391824 0.1428571 0.10714286 0.25000000
## 1798 0.5391824 0.1428571 0.10714286 0.25000000
## 1799 0.5391824 0.1428571 0.10714286 0.25000000
## 1800 0.5391824 0.1428571 0.10714286 0.25000000
## 1801 0.3120000 0.0000000 0.14285714 0.14285714
## 1802 0.3120000 0.0000000 0.14285714 0.14285714
## 1803 0.3120000 0.0000000 0.14285714 0.14285714
## 1804 0.3120000 0.0000000 0.14285714 0.14285714
## 1805 0.3120000 0.0000000 0.14285714 0.14285714
## 1806 0.3120000 0.0000000 0.14285714 0.14285714
## 1807 0.3120000 0.0000000 0.14285714 0.14285714
## 1808 0.3120000 0.0000000 0.14285714 0.14285714
## 1809 0.3120000 0.0000000 0.14285714 0.14285714
## 1810 0.3120000 0.0000000 0.14285714 0.14285714
## 1811 0.3120000 0.0000000 0.14285714 0.14285714
## 1812 0.3120000 0.0000000 0.14285714 0.14285714
## 1813 0.3120000 0.0000000 0.14285714 0.14285714
## 1814 0.3120000 0.0000000 0.14285714 0.14285714
## 1815 0.3120000 0.0000000 0.14285714 0.14285714
## 1816 0.3120000 0.0000000 0.14285714 0.14285714
## 1817 0.3120000 0.0000000 0.14285714 0.14285714
## 1818 0.3120000 0.0000000 0.14285714 0.14285714
## 1819 0.3120000 0.0000000 0.14285714 0.14285714
## 1820 0.3120000 0.0000000 0.14285714 0.14285714
## 1821 0.3120000 0.0000000 0.14285714 0.14285714
## 1822 0.3120000 0.0000000 0.14285714 0.14285714
## 1823 0.3120000 0.0000000 0.14285714 0.14285714
## 1824 0.3120000 0.0000000 0.14285714 0.14285714
## 1825 0.5950220 0.3333333 0.30303030 0.63636364
## 1826 0.5950220 0.3333333 0.30303030 0.63636364
## 1827 0.5950220 0.3333333 0.30303030 0.63636364
## 1828 0.5950220 0.3333333 0.30303030 0.63636364
## 1829 0.5950220 0.3333333 0.30303030 0.63636364
## 1830 0.5950220 0.3333333 0.30303030 0.63636364
## 1831 0.5950220 0.3333333 0.30303030 0.63636364
## 1832 0.5950220 0.3333333 0.30303030 0.63636364
## 1833 0.5950220 0.3333333 0.30303030 0.63636364
## 1834 0.5950220 0.3333333 0.30303030 0.63636364
## 1835 0.5950220 0.3333333 0.30303030 0.63636364
## 1836 0.5950220 0.3333333 0.30303030 0.63636364
## 1837 0.5950220 0.3333333 0.30303030 0.63636364
## 1838 0.5950220 0.3333333 0.30303030 0.63636364
## 1839 0.5950220 0.3333333 0.30303030 0.63636364
## 1840 0.5950220 0.3333333 0.30303030 0.63636364
## 1841 0.5950220 0.3333333 0.30303030 0.63636364
## 1842 0.5950220 0.3333333 0.30303030 0.63636364
## 1843 0.5950220 0.3333333 0.30303030 0.63636364
## 1844 0.5950220 0.3333333 0.30303030 0.63636364
## 1845 0.5950220 0.3333333 0.30303030 0.63636364
## 1846 0.5950220 0.3333333 0.30303030 0.63636364
## 1847 0.5950220 0.3333333 0.30303030 0.63636364
## 1848 0.5950220 0.3333333 0.30303030 0.63636364
## 1849 0.8314808 0.3333333 0.30303030 0.63636364
## 1850 0.8314808 0.3333333 0.30303030 0.63636364
## 1851 0.8314808 0.3333333 0.30303030 0.63636364
## 1852 0.8314808 0.3333333 0.30303030 0.63636364
## 1853 0.8314808 0.3333333 0.30303030 0.63636364
## 1854 0.8314808 0.3333333 0.30303030 0.63636364
## 1855 0.8314808 0.3333333 0.30303030 0.63636364
## 1856 0.8314808 0.3333333 0.30303030 0.63636364
## 1857 0.8314808 0.3333333 0.30303030 0.63636364
## 1858 0.8314808 0.3333333 0.30303030 0.63636364
## 1859 0.8314808 0.3333333 0.30303030 0.63636364
## 1860 0.8314808 0.3333333 0.30303030 0.63636364
## 1861 0.8314808 0.3333333 0.30303030 0.63636364
## 1862 0.8314808 0.3333333 0.30303030 0.63636364
## 1863 0.8314808 0.3333333 0.30303030 0.63636364
## 1864 0.8314808 0.3333333 0.30303030 0.63636364
## 1865 0.8314808 0.3333333 0.30303030 0.63636364
## 1866 0.8314808 0.3333333 0.30303030 0.63636364
## 1867 0.8314808 0.3333333 0.30303030 0.63636364
## 1868 0.8314808 0.3333333 0.30303030 0.63636364
## 1869 0.8314808 0.3333333 0.30303030 0.63636364
## 1870 0.8314808 0.3333333 0.30303030 0.63636364
## 1871 0.8314808 0.3333333 0.30303030 0.63636364
## 1872 0.8314808 0.3333333 0.30303030 0.63636364
## 1873 0.8227931 0.0000000 0.77777778 0.77777778
## 1874 0.8227931 0.0000000 0.77777778 0.77777778
## 1875 0.8227931 0.0000000 0.77777778 0.77777778
## 1876 0.8227931 0.0000000 0.77777778 0.77777778
## 1877 0.8227931 0.0000000 0.77777778 0.77777778
## 1878 0.8227931 0.0000000 0.77777778 0.77777778
## 1879 0.8227931 0.0000000 0.77777778 0.77777778
## 1880 0.8227931 0.0000000 0.77777778 0.77777778
## 1881 0.8227931 0.0000000 0.77777778 0.77777778
## 1882 0.8227931 0.0000000 0.77777778 0.77777778
## 1883 0.8227931 0.0000000 0.77777778 0.77777778
## 1884 0.8227931 0.0000000 0.77777778 0.77777778
## 1885 0.8227931 0.0000000 0.77777778 0.77777778
## 1886 0.8227931 0.0000000 0.77777778 0.77777778
## 1887 0.8227931 0.0000000 0.77777778 0.77777778
## 1888 0.8227931 0.0000000 0.77777778 0.77777778
## 1889 0.8227931 0.0000000 0.77777778 0.77777778
## 1890 0.8227931 0.0000000 0.77777778 0.77777778
## 1891 0.8227931 0.0000000 0.77777778 0.77777778
## 1892 0.8227931 0.0000000 0.77777778 0.77777778
## 1893 0.8227931 0.0000000 0.77777778 0.77777778
## 1894 0.8227931 0.0000000 0.77777778 0.77777778
## 1895 0.8227931 0.0000000 0.77777778 0.77777778
## 1896 0.8227931 0.0000000 0.77777778 0.77777778
## 1897 0.9043436 0.0000000 0.77777778 0.77777778
## 1898 0.9043436 0.0000000 0.77777778 0.77777778
## 1899 0.9043436 0.0000000 0.77777778 0.77777778
## 1900 0.9043436 0.0000000 0.77777778 0.77777778
## 1901 0.9043436 0.0000000 0.77777778 0.77777778
## 1902 0.9043436 0.0000000 0.77777778 0.77777778
## 1903 0.9043436 0.0000000 0.77777778 0.77777778
## 1904 0.9043436 0.0000000 0.77777778 0.77777778
## 1905 0.9043436 0.0000000 0.77777778 0.77777778
## 1906 0.9043436 0.0000000 0.77777778 0.77777778
## 1907 0.9043436 0.0000000 0.77777778 0.77777778
## 1908 0.9043436 0.0000000 0.77777778 0.77777778
## 1909 0.9043436 0.0000000 0.77777778 0.77777778
## 1910 0.9043436 0.0000000 0.77777778 0.77777778
## 1911 0.9043436 0.0000000 0.77777778 0.77777778
## 1912 0.9043436 0.0000000 0.77777778 0.77777778
## 1913 0.9043436 0.0000000 0.77777778 0.77777778
## 1914 0.9043436 0.0000000 0.77777778 0.77777778
## 1915 0.9043436 0.0000000 0.77777778 0.77777778
## 1916 0.9043436 0.0000000 0.77777778 0.77777778
## 1917 0.9043436 0.0000000 0.77777778 0.77777778
## 1918 0.9043436 0.0000000 0.77777778 0.77777778
## 1919 0.9043436 0.0000000 0.77777778 0.77777778
## 1920 0.9043436 0.0000000 0.77777778 0.77777778
## 1921 0.0000000 0.0000000 0.00000000 0.00000000
## 1922 0.0000000 0.0000000 0.00000000 0.00000000
## 1923 0.0000000 0.0000000 0.00000000 0.00000000
## 1924 0.0000000 0.0000000 0.00000000 0.00000000
## 1925 0.0000000 0.0000000 0.00000000 0.00000000
## 1926 0.0000000 0.0000000 0.00000000 0.00000000
## 1927 0.0000000 0.0000000 0.00000000 0.00000000
## 1928 0.0000000 0.0000000 0.00000000 0.00000000
## 1929 0.0000000 0.0000000 0.00000000 0.00000000
## 1930 0.0000000 0.0000000 0.00000000 0.00000000
## 1931 0.0000000 0.0000000 0.00000000 0.00000000
## 1932 0.0000000 0.0000000 0.00000000 0.00000000
## 1933 0.0000000 0.0000000 0.00000000 0.00000000
## 1934 0.0000000 0.0000000 0.00000000 0.00000000
## 1935 0.0000000 0.0000000 0.00000000 0.00000000
## 1936 0.0000000 0.0000000 0.00000000 0.00000000
## 1937 0.0000000 0.0000000 0.00000000 0.00000000
## 1938 0.0000000 0.0000000 0.00000000 0.00000000
## 1939 0.0000000 0.0000000 0.00000000 0.00000000
## 1940 0.0000000 0.0000000 0.00000000 0.00000000
## 1941 0.0000000 0.0000000 0.00000000 0.00000000
## 1942 0.0000000 0.0000000 0.00000000 0.00000000
## 1943 0.0000000 0.0000000 0.00000000 0.00000000
## 1944 0.0000000 0.0000000 0.00000000 0.00000000
## 1945 0.3027179 0.0000000 0.14285714 0.14285714
## 1946 0.3027179 0.0000000 0.14285714 0.14285714
## 1947 0.3027179 0.0000000 0.14285714 0.14285714
## 1948 0.3027179 0.0000000 0.14285714 0.14285714
## 1949 0.3027179 0.0000000 0.14285714 0.14285714
## 1950 0.3027179 0.0000000 0.14285714 0.14285714
## 1951 0.3027179 0.0000000 0.14285714 0.14285714
## 1952 0.3027179 0.0000000 0.14285714 0.14285714
## 1953 0.3027179 0.0000000 0.14285714 0.14285714
## 1954 0.3027179 0.0000000 0.14285714 0.14285714
## 1955 0.3027179 0.0000000 0.14285714 0.14285714
## 1956 0.3027179 0.0000000 0.14285714 0.14285714
## 1957 0.3027179 0.0000000 0.14285714 0.14285714
## 1958 0.3027179 0.0000000 0.14285714 0.14285714
## 1959 0.3027179 0.0000000 0.14285714 0.14285714
## 1960 0.3027179 0.0000000 0.14285714 0.14285714
## 1961 0.3027179 0.0000000 0.14285714 0.14285714
## 1962 0.3027179 0.0000000 0.14285714 0.14285714
## 1963 0.3027179 0.0000000 0.14285714 0.14285714
## 1964 0.3027179 0.0000000 0.14285714 0.14285714
## 1965 0.3027179 0.0000000 0.14285714 0.14285714
## 1966 0.3027179 0.0000000 0.14285714 0.14285714
## 1967 0.3027179 0.0000000 0.14285714 0.14285714
## 1968 0.3027179 0.0000000 0.14285714 0.14285714
## 1969 0.3534255 0.0000000 0.14285714 0.14285714
## 1970 0.3534255 0.0000000 0.14285714 0.14285714
## 1971 0.3534255 0.0000000 0.14285714 0.14285714
## 1972 0.3534255 0.0000000 0.14285714 0.14285714
## 1973 0.3534255 0.0000000 0.14285714 0.14285714
## 1974 0.3534255 0.0000000 0.14285714 0.14285714
## 1975 0.3534255 0.0000000 0.14285714 0.14285714
## 1976 0.3534255 0.0000000 0.14285714 0.14285714
## 1977 0.3534255 0.0000000 0.14285714 0.14285714
## 1978 0.3534255 0.0000000 0.14285714 0.14285714
## 1979 0.3534255 0.0000000 0.14285714 0.14285714
## 1980 0.3534255 0.0000000 0.14285714 0.14285714
## 1981 0.3534255 0.0000000 0.14285714 0.14285714
## 1982 0.3534255 0.0000000 0.14285714 0.14285714
## 1983 0.3534255 0.0000000 0.14285714 0.14285714
## 1984 0.3534255 0.0000000 0.14285714 0.14285714
## 1985 0.3534255 0.0000000 0.14285714 0.14285714
## 1986 0.3534255 0.0000000 0.14285714 0.14285714
## 1987 0.3534255 0.0000000 0.14285714 0.14285714
## 1988 0.3534255 0.0000000 0.14285714 0.14285714
## 1989 0.3534255 0.0000000 0.14285714 0.14285714
## 1990 0.3534255 0.0000000 0.14285714 0.14285714
## 1991 0.3534255 0.0000000 0.14285714 0.14285714
## 1992 0.3534255 0.0000000 0.14285714 0.14285714
## 1993 0.5300870 0.0000000 0.33333333 0.33333333
## 1994 0.5300870 0.0000000 0.33333333 0.33333333
## 1995 0.5300870 0.0000000 0.33333333 0.33333333
## 1996 0.5300870 0.0000000 0.33333333 0.33333333
## 1997 0.5300870 0.0000000 0.33333333 0.33333333
## 1998 0.5300870 0.0000000 0.33333333 0.33333333
## 1999 0.5300870 0.0000000 0.33333333 0.33333333
## 2000 0.5300870 0.0000000 0.33333333 0.33333333
## 2001 0.5300870 0.0000000 0.33333333 0.33333333
## 2002 0.5300870 0.0000000 0.33333333 0.33333333
## 2003 0.5300870 0.0000000 0.33333333 0.33333333
## 2004 0.5300870 0.0000000 0.33333333 0.33333333
## 2005 0.5300870 0.0000000 0.33333333 0.33333333
## 2006 0.5300870 0.0000000 0.33333333 0.33333333
## 2007 0.5300870 0.0000000 0.33333333 0.33333333
## 2008 0.5300870 0.0000000 0.33333333 0.33333333
## 2009 0.5300870 0.0000000 0.33333333 0.33333333
## 2010 0.5300870 0.0000000 0.33333333 0.33333333
## 2011 0.5300870 0.0000000 0.33333333 0.33333333
## 2012 0.5300870 0.0000000 0.33333333 0.33333333
## 2013 0.5300870 0.0000000 0.33333333 0.33333333
## 2014 0.5300870 0.0000000 0.33333333 0.33333333
## 2015 0.5300870 0.0000000 0.33333333 0.33333333
## 2016 0.5300870 0.0000000 0.33333333 0.33333333
## 2017 0.5106878 0.2500000 0.25000000 0.50000000
## 2018 0.5106878 0.2500000 0.25000000 0.50000000
## 2019 0.5106878 0.2500000 0.25000000 0.50000000
## 2020 0.5106878 0.2500000 0.25000000 0.50000000
## 2021 0.5106878 0.2500000 0.25000000 0.50000000
## 2022 0.5106878 0.2500000 0.25000000 0.50000000
## 2023 0.5106878 0.2500000 0.25000000 0.50000000
## 2024 0.5106878 0.2500000 0.25000000 0.50000000
## 2025 0.5106878 0.2500000 0.25000000 0.50000000
## 2026 0.5106878 0.2500000 0.25000000 0.50000000
## 2027 0.5106878 0.2500000 0.25000000 0.50000000
## 2028 0.5106878 0.2500000 0.25000000 0.50000000
## 2029 0.5106878 0.2500000 0.25000000 0.50000000
## 2030 0.5106878 0.2500000 0.25000000 0.50000000
## 2031 0.5106878 0.2500000 0.25000000 0.50000000
## 2032 0.5106878 0.2500000 0.25000000 0.50000000
## 2033 0.5106878 0.2500000 0.25000000 0.50000000
## 2034 0.5106878 0.2500000 0.25000000 0.50000000
## 2035 0.5106878 0.2500000 0.25000000 0.50000000
## 2036 0.5106878 0.2500000 0.25000000 0.50000000
## 2037 0.5106878 0.2500000 0.25000000 0.50000000
## 2038 0.5106878 0.2500000 0.25000000 0.50000000
## 2039 0.5106878 0.2500000 0.25000000 0.50000000
## 2040 0.5106878 0.2500000 0.25000000 0.50000000
## 2041 0.7580645 0.5000000 0.25000000 0.75000000
## 2042 0.7580645 0.5000000 0.25000000 0.75000000
## 2043 0.7580645 0.5000000 0.25000000 0.75000000
## 2044 0.7580645 0.5000000 0.25000000 0.75000000
## 2045 0.7580645 0.5000000 0.25000000 0.75000000
## 2046 0.7580645 0.5000000 0.25000000 0.75000000
## 2047 0.7580645 0.5000000 0.25000000 0.75000000
## 2048 0.7580645 0.5000000 0.25000000 0.75000000
## 2049 0.7580645 0.5000000 0.25000000 0.75000000
## 2050 0.7580645 0.5000000 0.25000000 0.75000000
## 2051 0.7580645 0.5000000 0.25000000 0.75000000
## 2052 0.7580645 0.5000000 0.25000000 0.75000000
## 2053 0.7580645 0.5000000 0.25000000 0.75000000
## 2054 0.7580645 0.5000000 0.25000000 0.75000000
## 2055 0.7580645 0.5000000 0.25000000 0.75000000
## 2056 0.7580645 0.5000000 0.25000000 0.75000000
## 2057 0.7580645 0.5000000 0.25000000 0.75000000
## 2058 0.7580645 0.5000000 0.25000000 0.75000000
## 2059 0.7580645 0.5000000 0.25000000 0.75000000
## 2060 0.7580645 0.5000000 0.25000000 0.75000000
## 2061 0.7580645 0.5000000 0.25000000 0.75000000
## 2062 0.7580645 0.5000000 0.25000000 0.75000000
## 2063 0.7580645 0.5000000 0.25000000 0.75000000
## 2064 0.7580645 0.5000000 0.25000000 0.75000000
## 2065 0.8084387 0.0000000 0.40000000 0.40000000
## 2066 0.8084387 0.0000000 0.40000000 0.40000000
## 2067 0.8084387 0.0000000 0.40000000 0.40000000
## 2068 0.8084387 0.0000000 0.40000000 0.40000000
## 2069 0.8084387 0.0000000 0.40000000 0.40000000
## 2070 0.8084387 0.0000000 0.40000000 0.40000000
## 2071 0.8084387 0.0000000 0.40000000 0.40000000
## 2072 0.8084387 0.0000000 0.40000000 0.40000000
## 2073 0.8084387 0.0000000 0.40000000 0.40000000
## 2074 0.8084387 0.0000000 0.40000000 0.40000000
## 2075 0.8084387 0.0000000 0.40000000 0.40000000
## 2076 0.8084387 0.0000000 0.40000000 0.40000000
## 2077 0.8084387 0.0000000 0.40000000 0.40000000
## 2078 0.8084387 0.0000000 0.40000000 0.40000000
## 2079 0.8084387 0.0000000 0.40000000 0.40000000
## 2080 0.8084387 0.0000000 0.40000000 0.40000000
## 2081 0.8084387 0.0000000 0.40000000 0.40000000
## 2082 0.8084387 0.0000000 0.40000000 0.40000000
## 2083 0.8084387 0.0000000 0.40000000 0.40000000
## 2084 0.8084387 0.0000000 0.40000000 0.40000000
## 2085 0.8084387 0.0000000 0.40000000 0.40000000
## 2086 0.8084387 0.0000000 0.40000000 0.40000000
## 2087 0.8084387 0.0000000 0.40000000 0.40000000
## 2088 0.8084387 0.0000000 0.40000000 0.40000000
## 2089 0.8082902 0.5000000 0.31818182 0.81818182
## 2090 0.8082902 0.5000000 0.31818182 0.81818182
## 2091 0.8082902 0.5000000 0.31818182 0.81818182
## 2092 0.8082902 0.5000000 0.31818182 0.81818182
## 2093 0.8082902 0.5000000 0.31818182 0.81818182
## 2094 0.8082902 0.5000000 0.31818182 0.81818182
## 2095 0.8082902 0.5000000 0.31818182 0.81818182
## 2096 0.8082902 0.5000000 0.31818182 0.81818182
## 2097 0.8082902 0.5000000 0.31818182 0.81818182
## 2098 0.8082902 0.5000000 0.31818182 0.81818182
## 2099 0.8082902 0.5000000 0.31818182 0.81818182
## 2100 0.8082902 0.5000000 0.31818182 0.81818182
## 2101 0.8082902 0.5000000 0.31818182 0.81818182
## 2102 0.8082902 0.5000000 0.31818182 0.81818182
## 2103 0.8082902 0.5000000 0.31818182 0.81818182
## 2104 0.8082902 0.5000000 0.31818182 0.81818182
## 2105 0.8082902 0.5000000 0.31818182 0.81818182
## 2106 0.8082902 0.5000000 0.31818182 0.81818182
## 2107 0.8082902 0.5000000 0.31818182 0.81818182
## 2108 0.8082902 0.5000000 0.31818182 0.81818182
## 2109 0.8082902 0.5000000 0.31818182 0.81818182
## 2110 0.8082902 0.5000000 0.31818182 0.81818182
## 2111 0.8082902 0.5000000 0.31818182 0.81818182
## 2112 0.8082902 0.5000000 0.31818182 0.81818182
## 2113 0.0000000 0.0000000 0.00000000 0.00000000
## 2114 0.0000000 0.0000000 0.00000000 0.00000000
## 2115 0.0000000 0.0000000 0.00000000 0.00000000
## 2116 0.0000000 0.0000000 0.00000000 0.00000000
## 2117 0.0000000 0.0000000 0.00000000 0.00000000
## 2118 0.0000000 0.0000000 0.00000000 0.00000000
## 2119 0.0000000 0.0000000 0.00000000 0.00000000
## 2120 0.0000000 0.0000000 0.00000000 0.00000000
## 2121 0.0000000 0.0000000 0.00000000 0.00000000
## 2122 0.0000000 0.0000000 0.00000000 0.00000000
## 2123 0.0000000 0.0000000 0.00000000 0.00000000
## 2124 0.0000000 0.0000000 0.00000000 0.00000000
## 2125 0.0000000 0.0000000 0.00000000 0.00000000
## 2126 0.0000000 0.0000000 0.00000000 0.00000000
## 2127 0.0000000 0.0000000 0.00000000 0.00000000
## 2128 0.0000000 0.0000000 0.00000000 0.00000000
## 2129 0.0000000 0.0000000 0.00000000 0.00000000
## 2130 0.0000000 0.0000000 0.00000000 0.00000000
## 2131 0.0000000 0.0000000 0.00000000 0.00000000
## 2132 0.0000000 0.0000000 0.00000000 0.00000000
## 2133 0.0000000 0.0000000 0.00000000 0.00000000
## 2134 0.0000000 0.0000000 0.00000000 0.00000000
## 2135 0.0000000 0.0000000 0.00000000 0.00000000
## 2136 0.0000000 0.0000000 0.00000000 0.00000000
## 2137 0.4274862 0.1666667 0.16666667 0.33333333
## 2138 0.4274862 0.1666667 0.16666667 0.33333333
## 2139 0.4274862 0.1666667 0.16666667 0.33333333
## 2140 0.4274862 0.1666667 0.16666667 0.33333333
## 2141 0.4274862 0.1666667 0.16666667 0.33333333
## 2142 0.4274862 0.1666667 0.16666667 0.33333333
## 2143 0.4274862 0.1666667 0.16666667 0.33333333
## 2144 0.4274862 0.1666667 0.16666667 0.33333333
## 2145 0.4274862 0.1666667 0.16666667 0.33333333
## 2146 0.4274862 0.1666667 0.16666667 0.33333333
## 2147 0.4274862 0.1666667 0.16666667 0.33333333
## 2148 0.4274862 0.1666667 0.16666667 0.33333333
## 2149 0.4274862 0.1666667 0.16666667 0.33333333
## 2150 0.4274862 0.1666667 0.16666667 0.33333333
## 2151 0.4274862 0.1666667 0.16666667 0.33333333
## 2152 0.4274862 0.1666667 0.16666667 0.33333333
## 2153 0.4274862 0.1666667 0.16666667 0.33333333
## 2154 0.4274862 0.1666667 0.16666667 0.33333333
## 2155 0.4274862 0.1666667 0.16666667 0.33333333
## 2156 0.4274862 0.1666667 0.16666667 0.33333333
## 2157 0.4274862 0.1666667 0.16666667 0.33333333
## 2158 0.4274862 0.1666667 0.16666667 0.33333333
## 2159 0.4274862 0.1666667 0.16666667 0.33333333
## 2160 0.4274862 0.1666667 0.16666667 0.33333333
## 2161 0.1717331 0.0000000 0.09090909 0.09090909
## 2162 0.1717331 0.0000000 0.09090909 0.09090909
## 2163 0.1717331 0.0000000 0.09090909 0.09090909
## 2164 0.1717331 0.0000000 0.09090909 0.09090909
## 2165 0.1717331 0.0000000 0.09090909 0.09090909
## 2166 0.1717331 0.0000000 0.09090909 0.09090909
## 2167 0.1717331 0.0000000 0.09090909 0.09090909
## 2168 0.1717331 0.0000000 0.09090909 0.09090909
## 2169 0.1717331 0.0000000 0.09090909 0.09090909
## 2170 0.1717331 0.0000000 0.09090909 0.09090909
## 2171 0.1717331 0.0000000 0.09090909 0.09090909
## 2172 0.1717331 0.0000000 0.09090909 0.09090909
## 2173 0.1717331 0.0000000 0.09090909 0.09090909
## 2174 0.1717331 0.0000000 0.09090909 0.09090909
## 2175 0.1717331 0.0000000 0.09090909 0.09090909
## 2176 0.1717331 0.0000000 0.09090909 0.09090909
## 2177 0.1717331 0.0000000 0.09090909 0.09090909
## 2178 0.1717331 0.0000000 0.09090909 0.09090909
## 2179 0.1717331 0.0000000 0.09090909 0.09090909
## 2180 0.1717331 0.0000000 0.09090909 0.09090909
## 2181 0.1717331 0.0000000 0.09090909 0.09090909
## 2182 0.1717331 0.0000000 0.09090909 0.09090909
## 2183 0.1717331 0.0000000 0.09090909 0.09090909
## 2184 0.1717331 0.0000000 0.09090909 0.09090909
## 2185 0.4019640 0.0000000 0.33333333 0.33333333
## 2186 0.4019640 0.0000000 0.33333333 0.33333333
## 2187 0.4019640 0.0000000 0.33333333 0.33333333
## 2188 0.4019640 0.0000000 0.33333333 0.33333333
## 2189 0.4019640 0.0000000 0.33333333 0.33333333
## 2190 0.4019640 0.0000000 0.33333333 0.33333333
## 2191 0.4019640 0.0000000 0.33333333 0.33333333
## 2192 0.4019640 0.0000000 0.33333333 0.33333333
## 2193 0.4019640 0.0000000 0.33333333 0.33333333
## 2194 0.4019640 0.0000000 0.33333333 0.33333333
## 2195 0.4019640 0.0000000 0.33333333 0.33333333
## 2196 0.4019640 0.0000000 0.33333333 0.33333333
## 2197 0.4019640 0.0000000 0.33333333 0.33333333
## 2198 0.4019640 0.0000000 0.33333333 0.33333333
## 2199 0.4019640 0.0000000 0.33333333 0.33333333
## 2200 0.4019640 0.0000000 0.33333333 0.33333333
## 2201 0.4019640 0.0000000 0.33333333 0.33333333
## 2202 0.4019640 0.0000000 0.33333333 0.33333333
## 2203 0.4019640 0.0000000 0.33333333 0.33333333
## 2204 0.4019640 0.0000000 0.33333333 0.33333333
## 2205 0.4019640 0.0000000 0.33333333 0.33333333
## 2206 0.4019640 0.0000000 0.33333333 0.33333333
## 2207 0.4019640 0.0000000 0.33333333 0.33333333
## 2208 0.4019640 0.0000000 0.33333333 0.33333333
## 2209 0.3756846 0.2500000 0.08333333 0.33333333
## 2210 0.3756846 0.2500000 0.08333333 0.33333333
## 2211 0.3756846 0.2500000 0.08333333 0.33333333
## 2212 0.3756846 0.2500000 0.08333333 0.33333333
## 2213 0.3756846 0.2500000 0.08333333 0.33333333
## 2214 0.3756846 0.2500000 0.08333333 0.33333333
## 2215 0.3756846 0.2500000 0.08333333 0.33333333
## 2216 0.3756846 0.2500000 0.08333333 0.33333333
## 2217 0.3756846 0.2500000 0.08333333 0.33333333
## 2218 0.3756846 0.2500000 0.08333333 0.33333333
## 2219 0.3756846 0.2500000 0.08333333 0.33333333
## 2220 0.3756846 0.2500000 0.08333333 0.33333333
## 2221 0.3756846 0.2500000 0.08333333 0.33333333
## 2222 0.3756846 0.2500000 0.08333333 0.33333333
## 2223 0.3756846 0.2500000 0.08333333 0.33333333
## 2224 0.3756846 0.2500000 0.08333333 0.33333333
## 2225 0.3756846 0.2500000 0.08333333 0.33333333
## 2226 0.3756846 0.2500000 0.08333333 0.33333333
## 2227 0.3756846 0.2500000 0.08333333 0.33333333
## 2228 0.3756846 0.2500000 0.08333333 0.33333333
## 2229 0.3756846 0.2500000 0.08333333 0.33333333
## 2230 0.3756846 0.2500000 0.08333333 0.33333333
## 2231 0.3756846 0.2500000 0.08333333 0.33333333
## 2232 0.3756846 0.2500000 0.08333333 0.33333333
## 2233 0.7278202 0.0000000 0.60000000 0.60000000
## 2234 0.7278202 0.0000000 0.60000000 0.60000000
## 2235 0.7278202 0.0000000 0.60000000 0.60000000
## 2236 0.7278202 0.0000000 0.60000000 0.60000000
## 2237 0.7278202 0.0000000 0.60000000 0.60000000
## 2238 0.7278202 0.0000000 0.60000000 0.60000000
## 2239 0.7278202 0.0000000 0.60000000 0.60000000
## 2240 0.7278202 0.0000000 0.60000000 0.60000000
## 2241 0.7278202 0.0000000 0.60000000 0.60000000
## 2242 0.7278202 0.0000000 0.60000000 0.60000000
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## 2244 0.7278202 0.0000000 0.60000000 0.60000000
## 2245 0.7278202 0.0000000 0.60000000 0.60000000
## 2246 0.7278202 0.0000000 0.60000000 0.60000000
## 2247 0.7278202 0.0000000 0.60000000 0.60000000
## 2248 0.7278202 0.0000000 0.60000000 0.60000000
## 2249 0.7278202 0.0000000 0.60000000 0.60000000
## 2250 0.7278202 0.0000000 0.60000000 0.60000000
## 2251 0.7278202 0.0000000 0.60000000 0.60000000
## 2252 0.7278202 0.0000000 0.60000000 0.60000000
## 2253 0.7278202 0.0000000 0.60000000 0.60000000
## 2254 0.7278202 0.0000000 0.60000000 0.60000000
## 2255 0.7278202 0.0000000 0.60000000 0.60000000
## 2256 0.7278202 0.0000000 0.60000000 0.60000000
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## 2258 0.8397072 0.0000000 0.40000000 0.40000000
## 2259 0.8397072 0.0000000 0.40000000 0.40000000
## 2260 0.8397072 0.0000000 0.40000000 0.40000000
## 2261 0.8397072 0.0000000 0.40000000 0.40000000
## 2262 0.8397072 0.0000000 0.40000000 0.40000000
## 2263 0.8397072 0.0000000 0.40000000 0.40000000
## 2264 0.8397072 0.0000000 0.40000000 0.40000000
## 2265 0.8397072 0.0000000 0.40000000 0.40000000
## 2266 0.8397072 0.0000000 0.40000000 0.40000000
## 2267 0.8397072 0.0000000 0.40000000 0.40000000
## 2268 0.8397072 0.0000000 0.40000000 0.40000000
## 2269 0.8397072 0.0000000 0.40000000 0.40000000
## 2270 0.8397072 0.0000000 0.40000000 0.40000000
## 2271 0.8397072 0.0000000 0.40000000 0.40000000
## 2272 0.8397072 0.0000000 0.40000000 0.40000000
## 2273 0.8397072 0.0000000 0.40000000 0.40000000
## 2274 0.8397072 0.0000000 0.40000000 0.40000000
## 2275 0.8397072 0.0000000 0.40000000 0.40000000
## 2276 0.8397072 0.0000000 0.40000000 0.40000000
## 2277 0.8397072 0.0000000 0.40000000 0.40000000
## 2278 0.8397072 0.0000000 0.40000000 0.40000000
## 2279 0.8397072 0.0000000 0.40000000 0.40000000
## 2280 0.8397072 0.0000000 0.40000000 0.40000000
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## 2282 0.7597403 0.5000000 0.27777778 0.77777778
## 2283 0.7597403 0.5000000 0.27777778 0.77777778
## 2284 0.7597403 0.5000000 0.27777778 0.77777778
## 2285 0.7597403 0.5000000 0.27777778 0.77777778
## 2286 0.7597403 0.5000000 0.27777778 0.77777778
## 2287 0.7597403 0.5000000 0.27777778 0.77777778
## 2288 0.7597403 0.5000000 0.27777778 0.77777778
## 2289 0.7597403 0.5000000 0.27777778 0.77777778
## 2290 0.7597403 0.5000000 0.27777778 0.77777778
## 2291 0.7597403 0.5000000 0.27777778 0.77777778
## 2292 0.7597403 0.5000000 0.27777778 0.77777778
## 2293 0.7597403 0.5000000 0.27777778 0.77777778
## 2294 0.7597403 0.5000000 0.27777778 0.77777778
## 2295 0.7597403 0.5000000 0.27777778 0.77777778
## 2296 0.7597403 0.5000000 0.27777778 0.77777778
## 2297 0.7597403 0.5000000 0.27777778 0.77777778
## 2298 0.7597403 0.5000000 0.27777778 0.77777778
## 2299 0.7597403 0.5000000 0.27777778 0.77777778
## 2300 0.7597403 0.5000000 0.27777778 0.77777778
## 2301 0.7597403 0.5000000 0.27777778 0.77777778
## 2302 0.7597403 0.5000000 0.27777778 0.77777778
## 2303 0.7597403 0.5000000 0.27777778 0.77777778
## 2304 0.7597403 0.5000000 0.27777778 0.77777778
## 2305 0.0000000 0.0000000 0.00000000 0.00000000
## 2306 0.0000000 0.0000000 0.00000000 0.00000000
## 2307 0.0000000 0.0000000 0.00000000 0.00000000
## 2308 0.0000000 0.0000000 0.00000000 0.00000000
## 2309 0.0000000 0.0000000 0.00000000 0.00000000
## 2310 0.0000000 0.0000000 0.00000000 0.00000000
## 2311 0.0000000 0.0000000 0.00000000 0.00000000
## 2312 0.0000000 0.0000000 0.00000000 0.00000000
## 2313 0.0000000 0.0000000 0.00000000 0.00000000
## 2314 0.0000000 0.0000000 0.00000000 0.00000000
## 2315 0.0000000 0.0000000 0.00000000 0.00000000
## 2316 0.0000000 0.0000000 0.00000000 0.00000000
## 2317 0.0000000 0.0000000 0.00000000 0.00000000
## 2318 0.0000000 0.0000000 0.00000000 0.00000000
## 2319 0.0000000 0.0000000 0.00000000 0.00000000
## 2320 0.0000000 0.0000000 0.00000000 0.00000000
## 2321 0.0000000 0.0000000 0.00000000 0.00000000
## 2322 0.0000000 0.0000000 0.00000000 0.00000000
## 2323 0.0000000 0.0000000 0.00000000 0.00000000
## 2324 0.0000000 0.0000000 0.00000000 0.00000000
## 2325 0.0000000 0.0000000 0.00000000 0.00000000
## 2326 0.0000000 0.0000000 0.00000000 0.00000000
## 2327 0.0000000 0.0000000 0.00000000 0.00000000
## 2328 0.0000000 0.0000000 0.00000000 0.00000000
## 2329 0.2390555 0.1666667 0.16666667 0.33333333
## 2330 0.2390555 0.1666667 0.16666667 0.33333333
## 2331 0.2390555 0.1666667 0.16666667 0.33333333
## 2332 0.2390555 0.1666667 0.16666667 0.33333333
## 2333 0.2390555 0.1666667 0.16666667 0.33333333
## 2334 0.2390555 0.1666667 0.16666667 0.33333333
## 2335 0.2390555 0.1666667 0.16666667 0.33333333
## 2336 0.2390555 0.1666667 0.16666667 0.33333333
## 2337 0.2390555 0.1666667 0.16666667 0.33333333
## 2338 0.2390555 0.1666667 0.16666667 0.33333333
## 2339 0.2390555 0.1666667 0.16666667 0.33333333
## 2340 0.2390555 0.1666667 0.16666667 0.33333333
## 2341 0.2390555 0.1666667 0.16666667 0.33333333
## 2342 0.2390555 0.1666667 0.16666667 0.33333333
## 2343 0.2390555 0.1666667 0.16666667 0.33333333
## 2344 0.2390555 0.1666667 0.16666667 0.33333333
## 2345 0.2390555 0.1666667 0.16666667 0.33333333
## 2346 0.2390555 0.1666667 0.16666667 0.33333333
## 2347 0.2390555 0.1666667 0.16666667 0.33333333
## 2348 0.2390555 0.1666667 0.16666667 0.33333333
## 2349 0.2390555 0.1666667 0.16666667 0.33333333
## 2350 0.2390555 0.1666667 0.16666667 0.33333333
## 2351 0.2390555 0.1666667 0.16666667 0.33333333
## 2352 0.2390555 0.1666667 0.16666667 0.33333333
## 2353 0.2484533 0.0000000 0.20000000 0.20000000
## 2354 0.2484533 0.0000000 0.20000000 0.20000000
## 2355 0.2484533 0.0000000 0.20000000 0.20000000
## 2356 0.2484533 0.0000000 0.20000000 0.20000000
## 2357 0.2484533 0.0000000 0.20000000 0.20000000
## 2358 0.2484533 0.0000000 0.20000000 0.20000000
## 2359 0.2484533 0.0000000 0.20000000 0.20000000
## 2360 0.2484533 0.0000000 0.20000000 0.20000000
## 2361 0.2484533 0.0000000 0.20000000 0.20000000
## 2362 0.2484533 0.0000000 0.20000000 0.20000000
## 2363 0.2484533 0.0000000 0.20000000 0.20000000
## 2364 0.2484533 0.0000000 0.20000000 0.20000000
## 2365 0.2484533 0.0000000 0.20000000 0.20000000
## 2366 0.2484533 0.0000000 0.20000000 0.20000000
## 2367 0.2484533 0.0000000 0.20000000 0.20000000
## 2368 0.2484533 0.0000000 0.20000000 0.20000000
## 2369 0.2484533 0.0000000 0.20000000 0.20000000
## 2370 0.2484533 0.0000000 0.20000000 0.20000000
## 2371 0.2484533 0.0000000 0.20000000 0.20000000
## 2372 0.2484533 0.0000000 0.20000000 0.20000000
## 2373 0.2484533 0.0000000 0.20000000 0.20000000
## 2374 0.2484533 0.0000000 0.20000000 0.20000000
## 2375 0.2484533 0.0000000 0.20000000 0.20000000
## 2376 0.2484533 0.0000000 0.20000000 0.20000000
## 2377 0.4900944 0.0000000 0.38461538 0.38461538
## 2378 0.4900944 0.0000000 0.38461538 0.38461538
## 2379 0.4900944 0.0000000 0.38461538 0.38461538
## 2380 0.4900944 0.0000000 0.38461538 0.38461538
## 2381 0.4900944 0.0000000 0.38461538 0.38461538
## 2382 0.4900944 0.0000000 0.38461538 0.38461538
## 2383 0.4900944 0.0000000 0.38461538 0.38461538
## 2384 0.4900944 0.0000000 0.38461538 0.38461538
## 2385 0.4900944 0.0000000 0.38461538 0.38461538
## 2386 0.4900944 0.0000000 0.38461538 0.38461538
## 2387 0.4900944 0.0000000 0.38461538 0.38461538
## 2388 0.4900944 0.0000000 0.38461538 0.38461538
## 2389 0.4900944 0.0000000 0.38461538 0.38461538
## 2390 0.4900944 0.0000000 0.38461538 0.38461538
## 2391 0.4900944 0.0000000 0.38461538 0.38461538
## 2392 0.4900944 0.0000000 0.38461538 0.38461538
## 2393 0.4900944 0.0000000 0.38461538 0.38461538
## 2394 0.4900944 0.0000000 0.38461538 0.38461538
## 2395 0.4900944 0.0000000 0.38461538 0.38461538
## 2396 0.4900944 0.0000000 0.38461538 0.38461538
## 2397 0.4900944 0.0000000 0.38461538 0.38461538
## 2398 0.4900944 0.0000000 0.38461538 0.38461538
## 2399 0.4900944 0.0000000 0.38461538 0.38461538
## 2400 0.4900944 0.0000000 0.38461538 0.38461538
## 2401 0.4155353 0.2500000 0.20454545 0.45454545
## 2402 0.4155353 0.2500000 0.20454545 0.45454545
## 2403 0.4155353 0.2500000 0.20454545 0.45454545
## 2404 0.4155353 0.2500000 0.20454545 0.45454545
## 2405 0.4155353 0.2500000 0.20454545 0.45454545
## 2406 0.4155353 0.2500000 0.20454545 0.45454545
## 2407 0.4155353 0.2500000 0.20454545 0.45454545
## 2408 0.4155353 0.2500000 0.20454545 0.45454545
## 2409 0.4155353 0.2500000 0.20454545 0.45454545
## 2410 0.4155353 0.2500000 0.20454545 0.45454545
## 2411 0.4155353 0.2500000 0.20454545 0.45454545
## 2412 0.4155353 0.2500000 0.20454545 0.45454545
## 2413 0.4155353 0.2500000 0.20454545 0.45454545
## 2414 0.4155353 0.2500000 0.20454545 0.45454545
## 2415 0.4155353 0.2500000 0.20454545 0.45454545
## 2416 0.4155353 0.2500000 0.20454545 0.45454545
## 2417 0.4155353 0.2500000 0.20454545 0.45454545
## 2418 0.4155353 0.2500000 0.20454545 0.45454545
## 2419 0.4155353 0.2500000 0.20454545 0.45454545
## 2420 0.4155353 0.2500000 0.20454545 0.45454545
## 2421 0.4155353 0.2500000 0.20454545 0.45454545
## 2422 0.4155353 0.2500000 0.20454545 0.45454545
## 2423 0.4155353 0.2500000 0.20454545 0.45454545
## 2424 0.4155353 0.2500000 0.20454545 0.45454545
## 2425 0.7878675 0.5000000 0.25000000 0.75000000
## 2426 0.7878675 0.5000000 0.25000000 0.75000000
## 2427 0.7878675 0.5000000 0.25000000 0.75000000
## 2428 0.7878675 0.5000000 0.25000000 0.75000000
## 2429 0.7878675 0.5000000 0.25000000 0.75000000
## 2430 0.7878675 0.5000000 0.25000000 0.75000000
## 2431 0.7878675 0.5000000 0.25000000 0.75000000
## 2432 0.7878675 0.5000000 0.25000000 0.75000000
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## 2434 0.7878675 0.5000000 0.25000000 0.75000000
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## 2436 0.7878675 0.5000000 0.25000000 0.75000000
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## 2438 0.7878675 0.5000000 0.25000000 0.75000000
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## 2447 0.7878675 0.5000000 0.25000000 0.75000000
## 2448 0.7878675 0.5000000 0.25000000 0.75000000
## 2449 0.7909868 0.0000000 0.45454545 0.45454545
## 2450 0.7909868 0.0000000 0.45454545 0.45454545
## 2451 0.7909868 0.0000000 0.45454545 0.45454545
## 2452 0.7909868 0.0000000 0.45454545 0.45454545
## 2453 0.7909868 0.0000000 0.45454545 0.45454545
## 2454 0.7909868 0.0000000 0.45454545 0.45454545
## 2455 0.7909868 0.0000000 0.45454545 0.45454545
## 2456 0.7909868 0.0000000 0.45454545 0.45454545
## 2457 0.7909868 0.0000000 0.45454545 0.45454545
## 2458 0.7909868 0.0000000 0.45454545 0.45454545
## 2459 0.7909868 0.0000000 0.45454545 0.45454545
## 2460 0.7909868 0.0000000 0.45454545 0.45454545
## 2461 0.7909868 0.0000000 0.45454545 0.45454545
## 2462 0.7909868 0.0000000 0.45454545 0.45454545
## 2463 0.7909868 0.0000000 0.45454545 0.45454545
## 2464 0.7909868 0.0000000 0.45454545 0.45454545
## 2465 0.7909868 0.0000000 0.45454545 0.45454545
## 2466 0.7909868 0.0000000 0.45454545 0.45454545
## 2467 0.7909868 0.0000000 0.45454545 0.45454545
## 2468 0.7909868 0.0000000 0.45454545 0.45454545
## 2469 0.7909868 0.0000000 0.45454545 0.45454545
## 2470 0.7909868 0.0000000 0.45454545 0.45454545
## 2471 0.7909868 0.0000000 0.45454545 0.45454545
## 2472 0.7909868 0.0000000 0.45454545 0.45454545
## 2473 0.8452490 0.5000000 0.27777778 0.77777778
## 2474 0.8452490 0.5000000 0.27777778 0.77777778
## 2475 0.8452490 0.5000000 0.27777778 0.77777778
## 2476 0.8452490 0.5000000 0.27777778 0.77777778
## 2477 0.8452490 0.5000000 0.27777778 0.77777778
## 2478 0.8452490 0.5000000 0.27777778 0.77777778
## 2479 0.8452490 0.5000000 0.27777778 0.77777778
## 2480 0.8452490 0.5000000 0.27777778 0.77777778
## 2481 0.8452490 0.5000000 0.27777778 0.77777778
## 2482 0.8452490 0.5000000 0.27777778 0.77777778
## 2483 0.8452490 0.5000000 0.27777778 0.77777778
## 2484 0.8452490 0.5000000 0.27777778 0.77777778
## 2485 0.8452490 0.5000000 0.27777778 0.77777778
## 2486 0.8452490 0.5000000 0.27777778 0.77777778
## 2487 0.8452490 0.5000000 0.27777778 0.77777778
## 2488 0.8452490 0.5000000 0.27777778 0.77777778
## 2489 0.8452490 0.5000000 0.27777778 0.77777778
## 2490 0.8452490 0.5000000 0.27777778 0.77777778
## 2491 0.8452490 0.5000000 0.27777778 0.77777778
## 2492 0.8452490 0.5000000 0.27777778 0.77777778
## 2493 0.8452490 0.5000000 0.27777778 0.77777778
## 2494 0.8452490 0.5000000 0.27777778 0.77777778
## 2495 0.8452490 0.5000000 0.27777778 0.77777778
## 2496 0.8452490 0.5000000 0.27777778 0.77777778
## 2497 0.0000000 0.0000000 0.00000000 0.00000000
## 2498 0.0000000 0.0000000 0.00000000 0.00000000
## 2499 0.0000000 0.0000000 0.00000000 0.00000000
## 2500 0.0000000 0.0000000 0.00000000 0.00000000
## 2501 0.0000000 0.0000000 0.00000000 0.00000000
## 2502 0.0000000 0.0000000 0.00000000 0.00000000
## 2503 0.0000000 0.0000000 0.00000000 0.00000000
## 2504 0.0000000 0.0000000 0.00000000 0.00000000
## 2505 0.0000000 0.0000000 0.00000000 0.00000000
## 2506 0.0000000 0.0000000 0.00000000 0.00000000
## 2507 0.0000000 0.0000000 0.00000000 0.00000000
## 2508 0.0000000 0.0000000 0.00000000 0.00000000
## 2509 0.0000000 0.0000000 0.00000000 0.00000000
## 2510 0.0000000 0.0000000 0.00000000 0.00000000
## 2511 0.0000000 0.0000000 0.00000000 0.00000000
## 2512 0.0000000 0.0000000 0.00000000 0.00000000
## 2513 0.0000000 0.0000000 0.00000000 0.00000000
## 2514 0.0000000 0.0000000 0.00000000 0.00000000
## 2515 0.0000000 0.0000000 0.00000000 0.00000000
## 2516 0.0000000 0.0000000 0.00000000 0.00000000
## 2517 0.0000000 0.0000000 0.00000000 0.00000000
## 2518 0.0000000 0.0000000 0.00000000 0.00000000
## 2519 0.0000000 0.0000000 0.00000000 0.00000000
## 2520 0.0000000 0.0000000 0.00000000 0.00000000
## 2521 0.2704892 0.0000000 0.07692308 0.07692308
## 2522 0.2704892 0.0000000 0.07692308 0.07692308
## 2523 0.2704892 0.0000000 0.07692308 0.07692308
## 2524 0.2704892 0.0000000 0.07692308 0.07692308
## 2525 0.2704892 0.0000000 0.07692308 0.07692308
## 2526 0.2704892 0.0000000 0.07692308 0.07692308
## 2527 0.2704892 0.0000000 0.07692308 0.07692308
## 2528 0.2704892 0.0000000 0.07692308 0.07692308
## 2529 0.2704892 0.0000000 0.07692308 0.07692308
## 2530 0.2704892 0.0000000 0.07692308 0.07692308
## 2531 0.2704892 0.0000000 0.07692308 0.07692308
## 2532 0.2704892 0.0000000 0.07692308 0.07692308
## 2533 0.2704892 0.0000000 0.07692308 0.07692308
## 2534 0.2704892 0.0000000 0.07692308 0.07692308
## 2535 0.2704892 0.0000000 0.07692308 0.07692308
## 2536 0.2704892 0.0000000 0.07692308 0.07692308
## 2537 0.2704892 0.0000000 0.07692308 0.07692308
## 2538 0.2704892 0.0000000 0.07692308 0.07692308
## 2539 0.2704892 0.0000000 0.07692308 0.07692308
## 2540 0.2704892 0.0000000 0.07692308 0.07692308
## 2541 0.2704892 0.0000000 0.07692308 0.07692308
## 2542 0.2704892 0.0000000 0.07692308 0.07692308
## 2543 0.2704892 0.0000000 0.07692308 0.07692308
## 2544 0.2704892 0.0000000 0.07692308 0.07692308
## 2545 0.3470454 0.0000000 0.14285714 0.14285714
## 2546 0.3470454 0.0000000 0.14285714 0.14285714
## 2547 0.3470454 0.0000000 0.14285714 0.14285714
## 2548 0.3470454 0.0000000 0.14285714 0.14285714
## 2549 0.3470454 0.0000000 0.14285714 0.14285714
## 2550 0.3470454 0.0000000 0.14285714 0.14285714
## 2551 0.3470454 0.0000000 0.14285714 0.14285714
## 2552 0.3470454 0.0000000 0.14285714 0.14285714
## 2553 0.3470454 0.0000000 0.14285714 0.14285714
## 2554 0.3470454 0.0000000 0.14285714 0.14285714
## 2555 0.3470454 0.0000000 0.14285714 0.14285714
## 2556 0.3470454 0.0000000 0.14285714 0.14285714
## 2557 0.3470454 0.0000000 0.14285714 0.14285714
## 2558 0.3470454 0.0000000 0.14285714 0.14285714
## 2559 0.3470454 0.0000000 0.14285714 0.14285714
## 2560 0.3470454 0.0000000 0.14285714 0.14285714
## 2561 0.3470454 0.0000000 0.14285714 0.14285714
## 2562 0.3470454 0.0000000 0.14285714 0.14285714
## 2563 0.3470454 0.0000000 0.14285714 0.14285714
## 2564 0.3470454 0.0000000 0.14285714 0.14285714
## 2565 0.3470454 0.0000000 0.14285714 0.14285714
## 2566 0.3470454 0.0000000 0.14285714 0.14285714
## 2567 0.3470454 0.0000000 0.14285714 0.14285714
## 2568 0.3470454 0.0000000 0.14285714 0.14285714
## 2569 0.1830536 0.2500000 0.15000000 0.40000000
## 2570 0.1830536 0.2500000 0.15000000 0.40000000
## 2571 0.1830536 0.2500000 0.15000000 0.40000000
## 2572 0.1830536 0.2500000 0.15000000 0.40000000
## 2573 0.1830536 0.2500000 0.15000000 0.40000000
## 2574 0.1830536 0.2500000 0.15000000 0.40000000
## 2575 0.1830536 0.2500000 0.15000000 0.40000000
## 2576 0.1830536 0.2500000 0.15000000 0.40000000
## 2577 0.1830536 0.2500000 0.15000000 0.40000000
## 2578 0.1830536 0.2500000 0.15000000 0.40000000
## 2579 0.1830536 0.2500000 0.15000000 0.40000000
## 2580 0.1830536 0.2500000 0.15000000 0.40000000
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## 2582 0.1830536 0.2500000 0.15000000 0.40000000
## 2583 0.1830536 0.2500000 0.15000000 0.40000000
## 2584 0.1830536 0.2500000 0.15000000 0.40000000
## 2585 0.1830536 0.2500000 0.15000000 0.40000000
## 2586 0.1830536 0.2500000 0.15000000 0.40000000
## 2587 0.1830536 0.2500000 0.15000000 0.40000000
## 2588 0.1830536 0.2500000 0.15000000 0.40000000
## 2589 0.1830536 0.2500000 0.15000000 0.40000000
## 2590 0.1830536 0.2500000 0.15000000 0.40000000
## 2591 0.1830536 0.2500000 0.15000000 0.40000000
## 2592 0.1830536 0.2500000 0.15000000 0.40000000
## 2593 0.4165868 0.2500000 0.15000000 0.40000000
## 2594 0.4165868 0.2500000 0.15000000 0.40000000
## 2595 0.4165868 0.2500000 0.15000000 0.40000000
## 2596 0.4165868 0.2500000 0.15000000 0.40000000
## 2597 0.4165868 0.2500000 0.15000000 0.40000000
## 2598 0.4165868 0.2500000 0.15000000 0.40000000
## 2599 0.4165868 0.2500000 0.15000000 0.40000000
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## 2601 0.4165868 0.2500000 0.15000000 0.40000000
## 2602 0.4165868 0.2500000 0.15000000 0.40000000
## 2603 0.4165868 0.2500000 0.15000000 0.40000000
## 2604 0.4165868 0.2500000 0.15000000 0.40000000
## 2605 0.4165868 0.2500000 0.15000000 0.40000000
## 2606 0.4165868 0.2500000 0.15000000 0.40000000
## 2607 0.4165868 0.2500000 0.15000000 0.40000000
## 2608 0.4165868 0.2500000 0.15000000 0.40000000
## 2609 0.4165868 0.2500000 0.15000000 0.40000000
## 2610 0.4165868 0.2500000 0.15000000 0.40000000
## 2611 0.4165868 0.2500000 0.15000000 0.40000000
## 2612 0.4165868 0.2500000 0.15000000 0.40000000
## 2613 0.4165868 0.2500000 0.15000000 0.40000000
## 2614 0.4165868 0.2500000 0.15000000 0.40000000
## 2615 0.4165868 0.2500000 0.15000000 0.40000000
## 2616 0.4165868 0.2500000 0.15000000 0.40000000
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## 2618 0.6847345 0.5000000 0.21428571 0.71428571
## 2619 0.6847345 0.5000000 0.21428571 0.71428571
## 2620 0.6847345 0.5000000 0.21428571 0.71428571
## 2621 0.6847345 0.5000000 0.21428571 0.71428571
## 2622 0.6847345 0.5000000 0.21428571 0.71428571
## 2623 0.6847345 0.5000000 0.21428571 0.71428571
## 2624 0.6847345 0.5000000 0.21428571 0.71428571
## 2625 0.6847345 0.5000000 0.21428571 0.71428571
## 2626 0.6847345 0.5000000 0.21428571 0.71428571
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## 2628 0.6847345 0.5000000 0.21428571 0.71428571
## 2629 0.6847345 0.5000000 0.21428571 0.71428571
## 2630 0.6847345 0.5000000 0.21428571 0.71428571
## 2631 0.6847345 0.5000000 0.21428571 0.71428571
## 2632 0.6847345 0.5000000 0.21428571 0.71428571
## 2633 0.6847345 0.5000000 0.21428571 0.71428571
## 2634 0.6847345 0.5000000 0.21428571 0.71428571
## 2635 0.6847345 0.5000000 0.21428571 0.71428571
## 2636 0.6847345 0.5000000 0.21428571 0.71428571
## 2637 0.6847345 0.5000000 0.21428571 0.71428571
## 2638 0.6847345 0.5000000 0.21428571 0.71428571
## 2639 0.6847345 0.5000000 0.21428571 0.71428571
## 2640 0.6847345 0.5000000 0.21428571 0.71428571
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## 2642 0.6820631 0.3333333 0.22222222 0.55555556
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## 2648 0.6820631 0.3333333 0.22222222 0.55555556
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## 2655 0.6820631 0.3333333 0.22222222 0.55555556
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## 2657 0.6820631 0.3333333 0.22222222 0.55555556
## 2658 0.6820631 0.3333333 0.22222222 0.55555556
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## 2661 0.6820631 0.3333333 0.22222222 0.55555556
## 2662 0.6820631 0.3333333 0.22222222 0.55555556
## 2663 0.6820631 0.3333333 0.22222222 0.55555556
## 2664 0.6820631 0.3333333 0.22222222 0.55555556
## 2665 0.5655391 0.5000000 0.21428571 0.71428571
## 2666 0.5655391 0.5000000 0.21428571 0.71428571
## 2667 0.5655391 0.5000000 0.21428571 0.71428571
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## 2677 0.5655391 0.5000000 0.21428571 0.71428571
## 2678 0.5655391 0.5000000 0.21428571 0.71428571
## 2679 0.5655391 0.5000000 0.21428571 0.71428571
## 2680 0.5655391 0.5000000 0.21428571 0.71428571
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## 2683 0.5655391 0.5000000 0.21428571 0.71428571
## 2684 0.5655391 0.5000000 0.21428571 0.71428571
## 2685 0.5655391 0.5000000 0.21428571 0.71428571
## 2686 0.5655391 0.5000000 0.21428571 0.71428571
## 2687 0.5655391 0.5000000 0.21428571 0.71428571
## 2688 0.5655391 0.5000000 0.21428571 0.71428571
## 2689 0.0000000 0.0000000 0.00000000 0.00000000
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## 2707 0.0000000 0.0000000 0.00000000 0.00000000
## 2708 0.0000000 0.0000000 0.00000000 0.00000000
## 2709 0.0000000 0.0000000 0.00000000 0.00000000
## 2710 0.0000000 0.0000000 0.00000000 0.00000000
## 2711 0.0000000 0.0000000 0.00000000 0.00000000
## 2712 0.0000000 0.0000000 0.00000000 0.00000000
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## 2714 0.5325091 0.0000000 0.20000000 0.20000000
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## 2716 0.5325091 0.0000000 0.20000000 0.20000000
## 2717 0.5325091 0.0000000 0.20000000 0.20000000
## 2718 0.5325091 0.0000000 0.20000000 0.20000000
## 2719 0.5325091 0.0000000 0.20000000 0.20000000
## 2720 0.5325091 0.0000000 0.20000000 0.20000000
## 2721 0.5325091 0.0000000 0.20000000 0.20000000
## 2722 0.5325091 0.0000000 0.20000000 0.20000000
## 2723 0.5325091 0.0000000 0.20000000 0.20000000
## 2724 0.5325091 0.0000000 0.20000000 0.20000000
## 2725 0.5325091 0.0000000 0.20000000 0.20000000
## 2726 0.5325091 0.0000000 0.20000000 0.20000000
## 2727 0.5325091 0.0000000 0.20000000 0.20000000
## 2728 0.5325091 0.0000000 0.20000000 0.20000000
## 2729 0.5325091 0.0000000 0.20000000 0.20000000
## 2730 0.5325091 0.0000000 0.20000000 0.20000000
## 2731 0.5325091 0.0000000 0.20000000 0.20000000
## 2732 0.5325091 0.0000000 0.20000000 0.20000000
## 2733 0.5325091 0.0000000 0.20000000 0.20000000
## 2734 0.5325091 0.0000000 0.20000000 0.20000000
## 2735 0.5325091 0.0000000 0.20000000 0.20000000
## 2736 0.5325091 0.0000000 0.20000000 0.20000000
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## 2738 0.2827829 0.0000000 0.07692308 0.07692308
## 2739 0.2827829 0.0000000 0.07692308 0.07692308
## 2740 0.2827829 0.0000000 0.07692308 0.07692308
## 2741 0.2827829 0.0000000 0.07692308 0.07692308
## 2742 0.2827829 0.0000000 0.07692308 0.07692308
## 2743 0.2827829 0.0000000 0.07692308 0.07692308
## 2744 0.2827829 0.0000000 0.07692308 0.07692308
## 2745 0.2827829 0.0000000 0.07692308 0.07692308
## 2746 0.2827829 0.0000000 0.07692308 0.07692308
## 2747 0.2827829 0.0000000 0.07692308 0.07692308
## 2748 0.2827829 0.0000000 0.07692308 0.07692308
## 2749 0.2827829 0.0000000 0.07692308 0.07692308
## 2750 0.2827829 0.0000000 0.07692308 0.07692308
## 2751 0.2827829 0.0000000 0.07692308 0.07692308
## 2752 0.2827829 0.0000000 0.07692308 0.07692308
## 2753 0.2827829 0.0000000 0.07692308 0.07692308
## 2754 0.2827829 0.0000000 0.07692308 0.07692308
## 2755 0.2827829 0.0000000 0.07692308 0.07692308
## 2756 0.2827829 0.0000000 0.07692308 0.07692308
## 2757 0.2827829 0.0000000 0.07692308 0.07692308
## 2758 0.2827829 0.0000000 0.07692308 0.07692308
## 2759 0.2827829 0.0000000 0.07692308 0.07692308
## 2760 0.2827829 0.0000000 0.07692308 0.07692308
## 2761 0.3693305 0.0000000 0.33333333 0.33333333
## 2762 0.3693305 0.0000000 0.33333333 0.33333333
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## 2765 0.3693305 0.0000000 0.33333333 0.33333333
## 2766 0.3693305 0.0000000 0.33333333 0.33333333
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## 2771 0.3693305 0.0000000 0.33333333 0.33333333
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## 2773 0.3693305 0.0000000 0.33333333 0.33333333
## 2774 0.3693305 0.0000000 0.33333333 0.33333333
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## 2777 0.3693305 0.0000000 0.33333333 0.33333333
## 2778 0.3693305 0.0000000 0.33333333 0.33333333
## 2779 0.3693305 0.0000000 0.33333333 0.33333333
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## 2781 0.3693305 0.0000000 0.33333333 0.33333333
## 2782 0.3693305 0.0000000 0.33333333 0.33333333
## 2783 0.3693305 0.0000000 0.33333333 0.33333333
## 2784 0.3693305 0.0000000 0.33333333 0.33333333
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## 2786 0.3697479 0.2500000 0.25000000 0.50000000
## 2787 0.3697479 0.2500000 0.25000000 0.50000000
## 2788 0.3697479 0.2500000 0.25000000 0.50000000
## 2789 0.3697479 0.2500000 0.25000000 0.50000000
## 2790 0.3697479 0.2500000 0.25000000 0.50000000
## 2791 0.3697479 0.2500000 0.25000000 0.50000000
## 2792 0.3697479 0.2500000 0.25000000 0.50000000
## 2793 0.3697479 0.2500000 0.25000000 0.50000000
## 2794 0.3697479 0.2500000 0.25000000 0.50000000
## 2795 0.3697479 0.2500000 0.25000000 0.50000000
## 2796 0.3697479 0.2500000 0.25000000 0.50000000
## 2797 0.3697479 0.2500000 0.25000000 0.50000000
## 2798 0.3697479 0.2500000 0.25000000 0.50000000
## 2799 0.3697479 0.2500000 0.25000000 0.50000000
## 2800 0.3697479 0.2500000 0.25000000 0.50000000
## 2801 0.3697479 0.2500000 0.25000000 0.50000000
## 2802 0.3697479 0.2500000 0.25000000 0.50000000
## 2803 0.3697479 0.2500000 0.25000000 0.50000000
## 2804 0.3697479 0.2500000 0.25000000 0.50000000
## 2805 0.3697479 0.2500000 0.25000000 0.50000000
## 2806 0.3697479 0.2500000 0.25000000 0.50000000
## 2807 0.3697479 0.2500000 0.25000000 0.50000000
## 2808 0.3697479 0.2500000 0.25000000 0.50000000
## 2809 0.7911323 0.5000000 0.30000000 0.80000000
## 2810 0.7911323 0.5000000 0.30000000 0.80000000
## 2811 0.7911323 0.5000000 0.30000000 0.80000000
## 2812 0.7911323 0.5000000 0.30000000 0.80000000
## 2813 0.7911323 0.5000000 0.30000000 0.80000000
## 2814 0.7911323 0.5000000 0.30000000 0.80000000
## 2815 0.7911323 0.5000000 0.30000000 0.80000000
## 2816 0.7911323 0.5000000 0.30000000 0.80000000
## 2817 0.7911323 0.5000000 0.30000000 0.80000000
## 2818 0.7911323 0.5000000 0.30000000 0.80000000
## 2819 0.7911323 0.5000000 0.30000000 0.80000000
## 2820 0.7911323 0.5000000 0.30000000 0.80000000
## 2821 0.7911323 0.5000000 0.30000000 0.80000000
## 2822 0.7911323 0.5000000 0.30000000 0.80000000
## 2823 0.7911323 0.5000000 0.30000000 0.80000000
## 2824 0.7911323 0.5000000 0.30000000 0.80000000
## 2825 0.7911323 0.5000000 0.30000000 0.80000000
## 2826 0.7911323 0.5000000 0.30000000 0.80000000
## 2827 0.7911323 0.5000000 0.30000000 0.80000000
## 2828 0.7911323 0.5000000 0.30000000 0.80000000
## 2829 0.7911323 0.5000000 0.30000000 0.80000000
## 2830 0.7911323 0.5000000 0.30000000 0.80000000
## 2831 0.7911323 0.5000000 0.30000000 0.80000000
## 2832 0.7911323 0.5000000 0.30000000 0.80000000
## 2833 0.8227931 0.0000000 0.45454545 0.45454545
## 2834 0.8227931 0.0000000 0.45454545 0.45454545
## 2835 0.8227931 0.0000000 0.45454545 0.45454545
## 2836 0.8227931 0.0000000 0.45454545 0.45454545
## 2837 0.8227931 0.0000000 0.45454545 0.45454545
## 2838 0.8227931 0.0000000 0.45454545 0.45454545
## 2839 0.8227931 0.0000000 0.45454545 0.45454545
## 2840 0.8227931 0.0000000 0.45454545 0.45454545
## 2841 0.8227931 0.0000000 0.45454545 0.45454545
## 2842 0.8227931 0.0000000 0.45454545 0.45454545
## 2843 0.8227931 0.0000000 0.45454545 0.45454545
## 2844 0.8227931 0.0000000 0.45454545 0.45454545
## 2845 0.8227931 0.0000000 0.45454545 0.45454545
## 2846 0.8227931 0.0000000 0.45454545 0.45454545
## 2847 0.8227931 0.0000000 0.45454545 0.45454545
## 2848 0.8227931 0.0000000 0.45454545 0.45454545
## 2849 0.8227931 0.0000000 0.45454545 0.45454545
## 2850 0.8227931 0.0000000 0.45454545 0.45454545
## 2851 0.8227931 0.0000000 0.45454545 0.45454545
## 2852 0.8227931 0.0000000 0.45454545 0.45454545
## 2853 0.8227931 0.0000000 0.45454545 0.45454545
## 2854 0.8227931 0.0000000 0.45454545 0.45454545
## 2855 0.8227931 0.0000000 0.45454545 0.45454545
## 2856 0.8227931 0.0000000 0.45454545 0.45454545
## 2857 0.8197869 0.5000000 0.30000000 0.80000000
## 2858 0.8197869 0.5000000 0.30000000 0.80000000
## 2859 0.8197869 0.5000000 0.30000000 0.80000000
## 2860 0.8197869 0.5000000 0.30000000 0.80000000
## 2861 0.8197869 0.5000000 0.30000000 0.80000000
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## 2863 0.8197869 0.5000000 0.30000000 0.80000000
## 2864 0.8197869 0.5000000 0.30000000 0.80000000
## 2865 0.8197869 0.5000000 0.30000000 0.80000000
## 2866 0.8197869 0.5000000 0.30000000 0.80000000
## 2867 0.8197869 0.5000000 0.30000000 0.80000000
## 2868 0.8197869 0.5000000 0.30000000 0.80000000
## 2869 0.8197869 0.5000000 0.30000000 0.80000000
## 2870 0.8197869 0.5000000 0.30000000 0.80000000
## 2871 0.8197869 0.5000000 0.30000000 0.80000000
## 2872 0.8197869 0.5000000 0.30000000 0.80000000
## 2873 0.8197869 0.5000000 0.30000000 0.80000000
## 2874 0.8197869 0.5000000 0.30000000 0.80000000
## 2875 0.8197869 0.5000000 0.30000000 0.80000000
## 2876 0.8197869 0.5000000 0.30000000 0.80000000
## 2877 0.8197869 0.5000000 0.30000000 0.80000000
## 2878 0.8197869 0.5000000 0.30000000 0.80000000
## 2879 0.8197869 0.5000000 0.30000000 0.80000000
## 2880 0.8197869 0.5000000 0.30000000 0.80000000
## 2881 0.0000000 0.0000000 0.00000000 0.00000000
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## 2888 0.0000000 0.0000000 0.00000000 0.00000000
## 2889 0.0000000 0.0000000 0.00000000 0.00000000
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## 2892 0.0000000 0.0000000 0.00000000 0.00000000
## 2893 0.0000000 0.0000000 0.00000000 0.00000000
## 2894 0.0000000 0.0000000 0.00000000 0.00000000
## 2895 0.0000000 0.0000000 0.00000000 0.00000000
## 2896 0.0000000 0.0000000 0.00000000 0.00000000
## 2897 0.0000000 0.0000000 0.00000000 0.00000000
## 2898 0.0000000 0.0000000 0.00000000 0.00000000
## 2899 0.0000000 0.0000000 0.00000000 0.00000000
## 2900 0.0000000 0.0000000 0.00000000 0.00000000
## 2901 0.0000000 0.0000000 0.00000000 0.00000000
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## 2903 0.0000000 0.0000000 0.00000000 0.00000000
## 2904 0.0000000 0.0000000 0.00000000 0.00000000
## 2905 0.2174229 0.1428571 0.05714286 0.20000000
## 2906 0.2174229 0.1428571 0.05714286 0.20000000
## 2907 0.2174229 0.1428571 0.05714286 0.20000000
## 2908 0.2174229 0.1428571 0.05714286 0.20000000
## 2909 0.2174229 0.1428571 0.05714286 0.20000000
## 2910 0.2174229 0.1428571 0.05714286 0.20000000
## 2911 0.2174229 0.1428571 0.05714286 0.20000000
## 2912 0.2174229 0.1428571 0.05714286 0.20000000
## 2913 0.2174229 0.1428571 0.05714286 0.20000000
## 2914 0.2174229 0.1428571 0.05714286 0.20000000
## 2915 0.2174229 0.1428571 0.05714286 0.20000000
## 2916 0.2174229 0.1428571 0.05714286 0.20000000
## 2917 0.2174229 0.1428571 0.05714286 0.20000000
## 2918 0.2174229 0.1428571 0.05714286 0.20000000
## 2919 0.2174229 0.1428571 0.05714286 0.20000000
## 2920 0.2174229 0.1428571 0.05714286 0.20000000
## 2921 0.2174229 0.1428571 0.05714286 0.20000000
## 2922 0.2174229 0.1428571 0.05714286 0.20000000
## 2923 0.2174229 0.1428571 0.05714286 0.20000000
## 2924 0.2174229 0.1428571 0.05714286 0.20000000
## 2925 0.2174229 0.1428571 0.05714286 0.20000000
## 2926 0.2174229 0.1428571 0.05714286 0.20000000
## 2927 0.2174229 0.1428571 0.05714286 0.20000000
## 2928 0.2174229 0.1428571 0.05714286 0.20000000
## 2929 0.2764012 0.2500000 0.00000000 0.25000000
## 2930 0.2764012 0.2500000 0.00000000 0.25000000
## 2931 0.2764012 0.2500000 0.00000000 0.25000000
## 2932 0.2764012 0.2500000 0.00000000 0.25000000
## 2933 0.2764012 0.2500000 0.00000000 0.25000000
## 2934 0.2764012 0.2500000 0.00000000 0.25000000
## 2935 0.2764012 0.2500000 0.00000000 0.25000000
## 2936 0.2764012 0.2500000 0.00000000 0.25000000
## 2937 0.2764012 0.2500000 0.00000000 0.25000000
## 2938 0.2764012 0.2500000 0.00000000 0.25000000
## 2939 0.2764012 0.2500000 0.00000000 0.25000000
## 2940 0.2764012 0.2500000 0.00000000 0.25000000
## 2941 0.2764012 0.2500000 0.00000000 0.25000000
## 2942 0.2764012 0.2500000 0.00000000 0.25000000
## 2943 0.2764012 0.2500000 0.00000000 0.25000000
## 2944 0.2764012 0.2500000 0.00000000 0.25000000
## 2945 0.2764012 0.2500000 0.00000000 0.25000000
## 2946 0.2764012 0.2500000 0.00000000 0.25000000
## 2947 0.2764012 0.2500000 0.00000000 0.25000000
## 2948 0.2764012 0.2500000 0.00000000 0.25000000
## 2949 0.2764012 0.2500000 0.00000000 0.25000000
## 2950 0.2764012 0.2500000 0.00000000 0.25000000
## 2951 0.2764012 0.2500000 0.00000000 0.25000000
## 2952 0.2764012 0.2500000 0.00000000 0.25000000
## 2953 0.5498699 0.0000000 0.60000000 0.60000000
## 2954 0.5498699 0.0000000 0.60000000 0.60000000
## 2955 0.5498699 0.0000000 0.60000000 0.60000000
## 2956 0.5498699 0.0000000 0.60000000 0.60000000
## 2957 0.5498699 0.0000000 0.60000000 0.60000000
## 2958 0.5498699 0.0000000 0.60000000 0.60000000
## 2959 0.5498699 0.0000000 0.60000000 0.60000000
## 2960 0.5498699 0.0000000 0.60000000 0.60000000
## 2961 0.5498699 0.0000000 0.60000000 0.60000000
## 2962 0.5498699 0.0000000 0.60000000 0.60000000
## 2963 0.5498699 0.0000000 0.60000000 0.60000000
## 2964 0.5498699 0.0000000 0.60000000 0.60000000
## 2965 0.5498699 0.0000000 0.60000000 0.60000000
## 2966 0.5498699 0.0000000 0.60000000 0.60000000
## 2967 0.5498699 0.0000000 0.60000000 0.60000000
## 2968 0.5498699 0.0000000 0.60000000 0.60000000
## 2969 0.5498699 0.0000000 0.60000000 0.60000000
## 2970 0.5498699 0.0000000 0.60000000 0.60000000
## 2971 0.5498699 0.0000000 0.60000000 0.60000000
## 2972 0.5498699 0.0000000 0.60000000 0.60000000
## 2973 0.5498699 0.0000000 0.60000000 0.60000000
## 2974 0.5498699 0.0000000 0.60000000 0.60000000
## 2975 0.5498699 0.0000000 0.60000000 0.60000000
## 2976 0.5498699 0.0000000 0.60000000 0.60000000
## 2977 0.3891789 0.0000000 0.33333333 0.33333333
## 2978 0.3891789 0.0000000 0.33333333 0.33333333
## 2979 0.3891789 0.0000000 0.33333333 0.33333333
## 2980 0.3891789 0.0000000 0.33333333 0.33333333
## 2981 0.3891789 0.0000000 0.33333333 0.33333333
## 2982 0.3891789 0.0000000 0.33333333 0.33333333
## 2983 0.3891789 0.0000000 0.33333333 0.33333333
## 2984 0.3891789 0.0000000 0.33333333 0.33333333
## 2985 0.3891789 0.0000000 0.33333333 0.33333333
## 2986 0.3891789 0.0000000 0.33333333 0.33333333
## 2987 0.3891789 0.0000000 0.33333333 0.33333333
## 2988 0.3891789 0.0000000 0.33333333 0.33333333
## 2989 0.3891789 0.0000000 0.33333333 0.33333333
## 2990 0.3891789 0.0000000 0.33333333 0.33333333
## 2991 0.3891789 0.0000000 0.33333333 0.33333333
## 2992 0.3891789 0.0000000 0.33333333 0.33333333
## 2993 0.3891789 0.0000000 0.33333333 0.33333333
## 2994 0.3891789 0.0000000 0.33333333 0.33333333
## 2995 0.3891789 0.0000000 0.33333333 0.33333333
## 2996 0.3891789 0.0000000 0.33333333 0.33333333
## 2997 0.3891789 0.0000000 0.33333333 0.33333333
## 2998 0.3891789 0.0000000 0.33333333 0.33333333
## 2999 0.3891789 0.0000000 0.33333333 0.33333333
## 3000 0.3891789 0.0000000 0.33333333 0.33333333
## 3001 0.6899874 0.0000000 0.33333333 0.33333333
## 3002 0.6899874 0.0000000 0.33333333 0.33333333
## 3003 0.6899874 0.0000000 0.33333333 0.33333333
## 3004 0.6899874 0.0000000 0.33333333 0.33333333
## 3005 0.6899874 0.0000000 0.33333333 0.33333333
## 3006 0.6899874 0.0000000 0.33333333 0.33333333
## 3007 0.6899874 0.0000000 0.33333333 0.33333333
## 3008 0.6899874 0.0000000 0.33333333 0.33333333
## 3009 0.6899874 0.0000000 0.33333333 0.33333333
## 3010 0.6899874 0.0000000 0.33333333 0.33333333
## 3011 0.6899874 0.0000000 0.33333333 0.33333333
## 3012 0.6899874 0.0000000 0.33333333 0.33333333
## 3013 0.6899874 0.0000000 0.33333333 0.33333333
## 3014 0.6899874 0.0000000 0.33333333 0.33333333
## 3015 0.6899874 0.0000000 0.33333333 0.33333333
## 3016 0.6899874 0.0000000 0.33333333 0.33333333
## 3017 0.6899874 0.0000000 0.33333333 0.33333333
## 3018 0.6899874 0.0000000 0.33333333 0.33333333
## 3019 0.6899874 0.0000000 0.33333333 0.33333333
## 3020 0.6899874 0.0000000 0.33333333 0.33333333
## 3021 0.6899874 0.0000000 0.33333333 0.33333333
## 3022 0.6899874 0.0000000 0.33333333 0.33333333
## 3023 0.6899874 0.0000000 0.33333333 0.33333333
## 3024 0.6899874 0.0000000 0.33333333 0.33333333
## 3025 0.8495744 0.5000000 0.27777778 0.77777778
## 3026 0.8495744 0.5000000 0.27777778 0.77777778
## 3027 0.8495744 0.5000000 0.27777778 0.77777778
## 3028 0.8495744 0.5000000 0.27777778 0.77777778
## 3029 0.8495744 0.5000000 0.27777778 0.77777778
## 3030 0.8495744 0.5000000 0.27777778 0.77777778
## 3031 0.8495744 0.5000000 0.27777778 0.77777778
## 3032 0.8495744 0.5000000 0.27777778 0.77777778
## 3033 0.8495744 0.5000000 0.27777778 0.77777778
## 3034 0.8495744 0.5000000 0.27777778 0.77777778
## 3035 0.8495744 0.5000000 0.27777778 0.77777778
## 3036 0.8495744 0.5000000 0.27777778 0.77777778
## 3037 0.8495744 0.5000000 0.27777778 0.77777778
## 3038 0.8495744 0.5000000 0.27777778 0.77777778
## 3039 0.8495744 0.5000000 0.27777778 0.77777778
## 3040 0.8495744 0.5000000 0.27777778 0.77777778
## 3041 0.8495744 0.5000000 0.27777778 0.77777778
## 3042 0.8495744 0.5000000 0.27777778 0.77777778
## 3043 0.8495744 0.5000000 0.27777778 0.77777778
## 3044 0.8495744 0.5000000 0.27777778 0.77777778
## 3045 0.8495744 0.5000000 0.27777778 0.77777778
## 3046 0.8495744 0.5000000 0.27777778 0.77777778
## 3047 0.8495744 0.5000000 0.27777778 0.77777778
## 3048 0.8495744 0.5000000 0.27777778 0.77777778
## 3049 0.7915983 0.0000000 0.28571429 0.28571429
## 3050 0.7915983 0.0000000 0.28571429 0.28571429
## 3051 0.7915983 0.0000000 0.28571429 0.28571429
## 3052 0.7915983 0.0000000 0.28571429 0.28571429
## 3053 0.7915983 0.0000000 0.28571429 0.28571429
## 3054 0.7915983 0.0000000 0.28571429 0.28571429
## 3055 0.7915983 0.0000000 0.28571429 0.28571429
## 3056 0.7915983 0.0000000 0.28571429 0.28571429
## 3057 0.7915983 0.0000000 0.28571429 0.28571429
## 3058 0.7915983 0.0000000 0.28571429 0.28571429
## 3059 0.7915983 0.0000000 0.28571429 0.28571429
## 3060 0.7915983 0.0000000 0.28571429 0.28571429
## 3061 0.7915983 0.0000000 0.28571429 0.28571429
## 3062 0.7915983 0.0000000 0.28571429 0.28571429
## 3063 0.7915983 0.0000000 0.28571429 0.28571429
## 3064 0.7915983 0.0000000 0.28571429 0.28571429
## 3065 0.7915983 0.0000000 0.28571429 0.28571429
## 3066 0.7915983 0.0000000 0.28571429 0.28571429
## 3067 0.7915983 0.0000000 0.28571429 0.28571429
## 3068 0.7915983 0.0000000 0.28571429 0.28571429
## 3069 0.7915983 0.0000000 0.28571429 0.28571429
## 3070 0.7915983 0.0000000 0.28571429 0.28571429
## 3071 0.7915983 0.0000000 0.28571429 0.28571429
## 3072 0.7915983 0.0000000 0.28571429 0.28571429
## 3073 0.0000000 0.0000000 0.00000000 0.00000000
## 3074 0.0000000 0.0000000 0.00000000 0.00000000
## 3075 0.0000000 0.0000000 0.00000000 0.00000000
## 3076 0.0000000 0.0000000 0.00000000 0.00000000
## 3077 0.0000000 0.0000000 0.00000000 0.00000000
## 3078 0.0000000 0.0000000 0.00000000 0.00000000
## 3079 0.0000000 0.0000000 0.00000000 0.00000000
## 3080 0.0000000 0.0000000 0.00000000 0.00000000
## 3081 0.0000000 0.0000000 0.00000000 0.00000000
## 3082 0.0000000 0.0000000 0.00000000 0.00000000
## 3083 0.0000000 0.0000000 0.00000000 0.00000000
## 3084 0.0000000 0.0000000 0.00000000 0.00000000
## 3085 0.0000000 0.0000000 0.00000000 0.00000000
## 3086 0.0000000 0.0000000 0.00000000 0.00000000
## 3087 0.0000000 0.0000000 0.00000000 0.00000000
## 3088 0.0000000 0.0000000 0.00000000 0.00000000
## 3089 0.0000000 0.0000000 0.00000000 0.00000000
## 3090 0.0000000 0.0000000 0.00000000 0.00000000
## 3091 0.0000000 0.0000000 0.00000000 0.00000000
## 3092 0.0000000 0.0000000 0.00000000 0.00000000
## 3093 0.0000000 0.0000000 0.00000000 0.00000000
## 3094 0.0000000 0.0000000 0.00000000 0.00000000
## 3095 0.0000000 0.0000000 0.00000000 0.00000000
## 3096 0.0000000 0.0000000 0.00000000 0.00000000
## 3097 0.4719528 0.1428571 0.10714286 0.25000000
## 3098 0.4719528 0.1428571 0.10714286 0.25000000
## 3099 0.4719528 0.1428571 0.10714286 0.25000000
## 3100 0.4719528 0.1428571 0.10714286 0.25000000
## 3101 0.4719528 0.1428571 0.10714286 0.25000000
## 3102 0.4719528 0.1428571 0.10714286 0.25000000
## 3103 0.4719528 0.1428571 0.10714286 0.25000000
## 3104 0.4719528 0.1428571 0.10714286 0.25000000
## 3105 0.4719528 0.1428571 0.10714286 0.25000000
## 3106 0.4719528 0.1428571 0.10714286 0.25000000
## 3107 0.4719528 0.1428571 0.10714286 0.25000000
## 3108 0.4719528 0.1428571 0.10714286 0.25000000
## 3109 0.4719528 0.1428571 0.10714286 0.25000000
## 3110 0.4719528 0.1428571 0.10714286 0.25000000
## 3111 0.4719528 0.1428571 0.10714286 0.25000000
## 3112 0.4719528 0.1428571 0.10714286 0.25000000
## 3113 0.4719528 0.1428571 0.10714286 0.25000000
## 3114 0.4719528 0.1428571 0.10714286 0.25000000
## 3115 0.4719528 0.1428571 0.10714286 0.25000000
## 3116 0.4719528 0.1428571 0.10714286 0.25000000
## 3117 0.4719528 0.1428571 0.10714286 0.25000000
## 3118 0.4719528 0.1428571 0.10714286 0.25000000
## 3119 0.4719528 0.1428571 0.10714286 0.25000000
## 3120 0.4719528 0.1428571 0.10714286 0.25000000
## 3121 0.2212978 0.0000000 0.23076923 0.23076923
## 3122 0.2212978 0.0000000 0.23076923 0.23076923
## 3123 0.2212978 0.0000000 0.23076923 0.23076923
## 3124 0.2212978 0.0000000 0.23076923 0.23076923
## 3125 0.2212978 0.0000000 0.23076923 0.23076923
## 3126 0.2212978 0.0000000 0.23076923 0.23076923
## 3127 0.2212978 0.0000000 0.23076923 0.23076923
## 3128 0.2212978 0.0000000 0.23076923 0.23076923
## 3129 0.2212978 0.0000000 0.23076923 0.23076923
## 3130 0.2212978 0.0000000 0.23076923 0.23076923
## 3131 0.2212978 0.0000000 0.23076923 0.23076923
## 3132 0.2212978 0.0000000 0.23076923 0.23076923
## 3133 0.2212978 0.0000000 0.23076923 0.23076923
## 3134 0.2212978 0.0000000 0.23076923 0.23076923
## 3135 0.2212978 0.0000000 0.23076923 0.23076923
## 3136 0.2212978 0.0000000 0.23076923 0.23076923
## 3137 0.2212978 0.0000000 0.23076923 0.23076923
## 3138 0.2212978 0.0000000 0.23076923 0.23076923
## 3139 0.2212978 0.0000000 0.23076923 0.23076923
## 3140 0.2212978 0.0000000 0.23076923 0.23076923
## 3141 0.2212978 0.0000000 0.23076923 0.23076923
## 3142 0.2212978 0.0000000 0.23076923 0.23076923
## 3143 0.2212978 0.0000000 0.23076923 0.23076923
## 3144 0.2212978 0.0000000 0.23076923 0.23076923
## 3145 0.6384138 0.0000000 0.60000000 0.60000000
## 3146 0.6384138 0.0000000 0.60000000 0.60000000
## 3147 0.6384138 0.0000000 0.60000000 0.60000000
## 3148 0.6384138 0.0000000 0.60000000 0.60000000
## 3149 0.6384138 0.0000000 0.60000000 0.60000000
## 3150 0.6384138 0.0000000 0.60000000 0.60000000
## 3151 0.6384138 0.0000000 0.60000000 0.60000000
## 3152 0.6384138 0.0000000 0.60000000 0.60000000
## 3153 0.6384138 0.0000000 0.60000000 0.60000000
## 3154 0.6384138 0.0000000 0.60000000 0.60000000
## 3155 0.6384138 0.0000000 0.60000000 0.60000000
## 3156 0.6384138 0.0000000 0.60000000 0.60000000
## 3157 0.6384138 0.0000000 0.60000000 0.60000000
## 3158 0.6384138 0.0000000 0.60000000 0.60000000
## 3159 0.6384138 0.0000000 0.60000000 0.60000000
## 3160 0.6384138 0.0000000 0.60000000 0.60000000
## 3161 0.6384138 0.0000000 0.60000000 0.60000000
## 3162 0.6384138 0.0000000 0.60000000 0.60000000
## 3163 0.6384138 0.0000000 0.60000000 0.60000000
## 3164 0.6384138 0.0000000 0.60000000 0.60000000
## 3165 0.6384138 0.0000000 0.60000000 0.60000000
## 3166 0.6384138 0.0000000 0.60000000 0.60000000
## 3167 0.6384138 0.0000000 0.60000000 0.60000000
## 3168 0.6384138 0.0000000 0.60000000 0.60000000
## 3169 0.5259003 0.2500000 0.08333333 0.33333333
## 3170 0.5259003 0.2500000 0.08333333 0.33333333
## 3171 0.5259003 0.2500000 0.08333333 0.33333333
## 3172 0.5259003 0.2500000 0.08333333 0.33333333
## 3173 0.5259003 0.2500000 0.08333333 0.33333333
## 3174 0.5259003 0.2500000 0.08333333 0.33333333
## 3175 0.5259003 0.2500000 0.08333333 0.33333333
## 3176 0.5259003 0.2500000 0.08333333 0.33333333
## 3177 0.5259003 0.2500000 0.08333333 0.33333333
## 3178 0.5259003 0.2500000 0.08333333 0.33333333
## 3179 0.5259003 0.2500000 0.08333333 0.33333333
## 3180 0.5259003 0.2500000 0.08333333 0.33333333
## 3181 0.5259003 0.2500000 0.08333333 0.33333333
## 3182 0.5259003 0.2500000 0.08333333 0.33333333
## 3183 0.5259003 0.2500000 0.08333333 0.33333333
## 3184 0.5259003 0.2500000 0.08333333 0.33333333
## 3185 0.5259003 0.2500000 0.08333333 0.33333333
## 3186 0.5259003 0.2500000 0.08333333 0.33333333
## 3187 0.5259003 0.2500000 0.08333333 0.33333333
## 3188 0.5259003 0.2500000 0.08333333 0.33333333
## 3189 0.5259003 0.2500000 0.08333333 0.33333333
## 3190 0.5259003 0.2500000 0.08333333 0.33333333
## 3191 0.5259003 0.2500000 0.08333333 0.33333333
## 3192 0.5259003 0.2500000 0.08333333 0.33333333
## 3193 0.7065821 0.0000000 0.45454545 0.45454545
## 3194 0.7065821 0.0000000 0.45454545 0.45454545
## 3195 0.7065821 0.0000000 0.45454545 0.45454545
## 3196 0.7065821 0.0000000 0.45454545 0.45454545
## 3197 0.7065821 0.0000000 0.45454545 0.45454545
## 3198 0.7065821 0.0000000 0.45454545 0.45454545
## 3199 0.7065821 0.0000000 0.45454545 0.45454545
## 3200 0.7065821 0.0000000 0.45454545 0.45454545
## 3201 0.7065821 0.0000000 0.45454545 0.45454545
## 3202 0.7065821 0.0000000 0.45454545 0.45454545
## 3203 0.7065821 0.0000000 0.45454545 0.45454545
## 3204 0.7065821 0.0000000 0.45454545 0.45454545
## 3205 0.7065821 0.0000000 0.45454545 0.45454545
## 3206 0.7065821 0.0000000 0.45454545 0.45454545
## 3207 0.7065821 0.0000000 0.45454545 0.45454545
## 3208 0.7065821 0.0000000 0.45454545 0.45454545
## 3209 0.7065821 0.0000000 0.45454545 0.45454545
## 3210 0.7065821 0.0000000 0.45454545 0.45454545
## 3211 0.7065821 0.0000000 0.45454545 0.45454545
## 3212 0.7065821 0.0000000 0.45454545 0.45454545
## 3213 0.7065821 0.0000000 0.45454545 0.45454545
## 3214 0.7065821 0.0000000 0.45454545 0.45454545
## 3215 0.7065821 0.0000000 0.45454545 0.45454545
## 3216 0.7065821 0.0000000 0.45454545 0.45454545
## 3217 0.7709188 0.0000000 0.55555556 0.55555556
## 3218 0.7709188 0.0000000 0.55555556 0.55555556
## 3219 0.7709188 0.0000000 0.55555556 0.55555556
## 3220 0.7709188 0.0000000 0.55555556 0.55555556
## 3221 0.7709188 0.0000000 0.55555556 0.55555556
## 3222 0.7709188 0.0000000 0.55555556 0.55555556
## 3223 0.7709188 0.0000000 0.55555556 0.55555556
## 3224 0.7709188 0.0000000 0.55555556 0.55555556
## 3225 0.7709188 0.0000000 0.55555556 0.55555556
## metaecosystem_richness total_metaecosystem_bioarea_mm2
## 1 11 96.92197
## 2 11 96.92197
## 3 11 96.92197
## 4 11 96.92197
## 5 11 96.92197
## 6 11 96.92197
## 7 11 96.92197
## 8 11 96.92197
## 9 11 96.92197
## 10 11 96.92197
## 11 11 96.92197
## 12 11 96.92197
## 13 11 96.92197
## 14 11 96.92197
## 15 11 96.92197
## 16 11 96.92197
## 17 11 96.92197
## 18 11 96.92197
## 19 11 96.92197
## 20 11 96.92197
## 21 11 96.92197
## 22 11 96.92197
## 23 11 96.92197
## 24 11 96.92197
## 25 9 152.90836
## 26 9 152.90836
## 27 9 152.90836
## 28 9 152.90836
## 29 9 152.90836
## 30 9 152.90836
## 31 9 152.90836
## 32 9 152.90836
## 33 9 152.90836
## 34 9 152.90836
## 35 9 152.90836
## 36 9 152.90836
## 37 9 152.90836
## 38 9 152.90836
## 39 9 152.90836
## 40 9 152.90836
## 41 9 152.90836
## 42 9 152.90836
## 43 9 152.90836
## 44 9 152.90836
## 45 9 152.90836
## 46 9 152.90836
## 47 9 152.90836
## 48 9 152.90836
## 49 9 163.09305
## 50 9 163.09305
## 51 9 163.09305
## 52 9 163.09305
## 53 9 163.09305
## 54 9 163.09305
## 55 9 163.09305
## 56 9 163.09305
## 57 9 163.09305
## 58 9 163.09305
## 59 9 163.09305
## 60 9 163.09305
## 61 9 163.09305
## 62 9 163.09305
## 63 9 163.09305
## 64 9 163.09305
## 65 9 163.09305
## 66 9 163.09305
## 67 9 163.09305
## 68 9 163.09305
## 69 9 163.09305
## 70 9 163.09305
## 71 9 163.09305
## 72 9 163.09305
## 73 8 182.03030
## 74 8 182.03030
## 75 8 182.03030
## 76 8 182.03030
## 77 8 182.03030
## 78 8 182.03030
## 79 8 182.03030
## 80 8 182.03030
## 81 8 182.03030
## 82 8 182.03030
## 83 8 182.03030
## 84 8 182.03030
## 85 8 182.03030
## 86 8 182.03030
## 87 8 182.03030
## 88 8 182.03030
## 89 8 182.03030
## 90 8 182.03030
## 91 8 182.03030
## 92 8 182.03030
## 93 8 182.03030
## 94 8 182.03030
## 95 8 182.03030
## 96 8 182.03030
## 97 9 140.28580
## 98 9 140.28580
## 99 9 140.28580
## 100 9 140.28580
## 101 9 140.28580
## 102 9 140.28580
## 103 9 140.28580
## 104 9 140.28580
## 105 9 140.28580
## 106 9 140.28580
## 107 9 140.28580
## 108 9 140.28580
## 109 9 140.28580
## 110 9 140.28580
## 111 9 140.28580
## 112 9 140.28580
## 113 9 140.28580
## 114 9 140.28580
## 115 9 140.28580
## 116 9 140.28580
## 117 9 140.28580
## 118 9 140.28580
## 119 9 140.28580
## 120 9 140.28580
## 121 6 117.28324
## 122 6 117.28324
## 123 6 117.28324
## 124 6 117.28324
## 125 6 117.28324
## 126 6 117.28324
## 127 6 117.28324
## 128 6 117.28324
## 129 6 117.28324
## 130 6 117.28324
## 131 6 117.28324
## 132 6 117.28324
## 133 6 117.28324
## 134 6 117.28324
## 135 6 117.28324
## 136 6 117.28324
## 137 6 117.28324
## 138 6 117.28324
## 139 6 117.28324
## 140 6 117.28324
## 141 6 117.28324
## 142 6 117.28324
## 143 6 117.28324
## 144 6 117.28324
## 145 9 103.80974
## 146 9 103.80974
## 147 9 103.80974
## 148 9 103.80974
## 149 9 103.80974
## 150 9 103.80974
## 151 9 103.80974
## 152 9 103.80974
## 153 9 103.80974
## 154 9 103.80974
## 155 9 103.80974
## 156 9 103.80974
## 157 9 103.80974
## 158 9 103.80974
## 159 9 103.80974
## 160 9 103.80974
## 161 9 103.80974
## 162 9 103.80974
## 163 9 103.80974
## 164 9 103.80974
## 165 9 103.80974
## 166 9 103.80974
## 167 9 103.80974
## 168 9 103.80974
## 169 9 92.60172
## 170 9 92.60172
## 171 9 92.60172
## 172 9 92.60172
## 173 9 92.60172
## 174 9 92.60172
## 175 9 92.60172
## 176 9 92.60172
## 177 9 92.60172
## 178 9 92.60172
## 179 9 92.60172
## 180 9 92.60172
## 181 9 92.60172
## 182 9 92.60172
## 183 9 92.60172
## 184 9 92.60172
## 185 9 92.60172
## 186 9 92.60172
## 187 9 92.60172
## 188 9 92.60172
## 189 9 92.60172
## 190 9 92.60172
## 191 9 92.60172
## 192 9 92.60172
## 193 11 96.92197
## 194 11 96.92197
## 195 11 96.92197
## 196 11 96.92197
## 197 11 96.92197
## 198 11 96.92197
## 199 11 96.92197
## 200 11 96.92197
## 201 11 96.92197
## 202 11 96.92197
## 203 11 96.92197
## 204 11 96.92197
## 205 11 96.92197
## 206 11 96.92197
## 207 11 96.92197
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## 2718 9 119.13585
## 2719 9 119.13585
## 2720 9 119.13585
## 2721 9 119.13585
## 2722 9 119.13585
## 2723 9 119.13585
## 2724 9 119.13585
## 2725 9 119.13585
## 2726 9 119.13585
## 2727 9 119.13585
## 2728 9 119.13585
## 2729 9 119.13585
## 2730 9 119.13585
## 2731 9 119.13585
## 2732 9 119.13585
## 2733 9 119.13585
## 2734 9 119.13585
## 2735 9 119.13585
## 2736 9 119.13585
## 2737 7 149.70690
## 2738 7 149.70690
## 2739 7 149.70690
## 2740 7 149.70690
## 2741 7 149.70690
## 2742 7 149.70690
## 2743 7 149.70690
## 2744 7 149.70690
## 2745 7 149.70690
## 2746 7 149.70690
## 2747 7 149.70690
## 2748 7 149.70690
## 2749 7 149.70690
## 2750 7 149.70690
## 2751 7 149.70690
## 2752 7 149.70690
## 2753 7 149.70690
## 2754 7 149.70690
## 2755 7 149.70690
## 2756 7 149.70690
## 2757 7 149.70690
## 2758 7 149.70690
## 2759 7 149.70690
## 2760 7 149.70690
## 2761 8 205.19359
## 2762 8 205.19359
## 2763 8 205.19359
## 2764 8 205.19359
## 2765 8 205.19359
## 2766 8 205.19359
## 2767 8 205.19359
## 2768 8 205.19359
## 2769 8 205.19359
## 2770 8 205.19359
## 2771 8 205.19359
## 2772 8 205.19359
## 2773 8 205.19359
## 2774 8 205.19359
## 2775 8 205.19359
## 2776 8 205.19359
## 2777 8 205.19359
## 2778 8 205.19359
## 2779 8 205.19359
## 2780 8 205.19359
## 2781 8 205.19359
## 2782 8 205.19359
## 2783 8 205.19359
## 2784 8 205.19359
## 2785 9 210.11345
## 2786 9 210.11345
## 2787 9 210.11345
## 2788 9 210.11345
## 2789 9 210.11345
## 2790 9 210.11345
## 2791 9 210.11345
## 2792 9 210.11345
## 2793 9 210.11345
## 2794 9 210.11345
## 2795 9 210.11345
## 2796 9 210.11345
## 2797 9 210.11345
## 2798 9 210.11345
## 2799 9 210.11345
## 2800 9 210.11345
## 2801 9 210.11345
## 2802 9 210.11345
## 2803 9 210.11345
## 2804 9 210.11345
## 2805 9 210.11345
## 2806 9 210.11345
## 2807 9 210.11345
## 2808 9 210.11345
## 2809 9 170.39894
## 2810 9 170.39894
## 2811 9 170.39894
## 2812 9 170.39894
## 2813 9 170.39894
## 2814 9 170.39894
## 2815 9 170.39894
## 2816 9 170.39894
## 2817 9 170.39894
## 2818 9 170.39894
## 2819 9 170.39894
## 2820 9 170.39894
## 2821 9 170.39894
## 2822 9 170.39894
## 2823 9 170.39894
## 2824 9 170.39894
## 2825 9 170.39894
## 2826 9 170.39894
## 2827 9 170.39894
## 2828 9 170.39894
## 2829 9 170.39894
## 2830 9 170.39894
## 2831 9 170.39894
## 2832 9 170.39894
## 2833 8 149.41666
## 2834 8 149.41666
## 2835 8 149.41666
## 2836 8 149.41666
## 2837 8 149.41666
## 2838 8 149.41666
## 2839 8 149.41666
## 2840 8 149.41666
## 2841 8 149.41666
## 2842 8 149.41666
## 2843 8 149.41666
## 2844 8 149.41666
## 2845 8 149.41666
## 2846 8 149.41666
## 2847 8 149.41666
## 2848 8 149.41666
## 2849 8 149.41666
## 2850 8 149.41666
## 2851 8 149.41666
## 2852 8 149.41666
## 2853 8 149.41666
## 2854 8 149.41666
## 2855 8 149.41666
## 2856 8 149.41666
## 2857 9 111.86388
## 2858 9 111.86388
## 2859 9 111.86388
## 2860 9 111.86388
## 2861 9 111.86388
## 2862 9 111.86388
## 2863 9 111.86388
## 2864 9 111.86388
## 2865 9 111.86388
## 2866 9 111.86388
## 2867 9 111.86388
## 2868 9 111.86388
## 2869 9 111.86388
## 2870 9 111.86388
## 2871 9 111.86388
## 2872 9 111.86388
## 2873 9 111.86388
## 2874 9 111.86388
## 2875 9 111.86388
## 2876 9 111.86388
## 2877 9 111.86388
## 2878 9 111.86388
## 2879 9 111.86388
## 2880 9 111.86388
## 2881 11 96.92197
## 2882 11 96.92197
## 2883 11 96.92197
## 2884 11 96.92197
## 2885 11 96.92197
## 2886 11 96.92197
## 2887 11 96.92197
## 2888 11 96.92197
## 2889 11 96.92197
## 2890 11 96.92197
## 2891 11 96.92197
## 2892 11 96.92197
## 2893 11 96.92197
## 2894 11 96.92197
## 2895 11 96.92197
## 2896 11 96.92197
## 2897 11 96.92197
## 2898 11 96.92197
## 2899 11 96.92197
## 2900 11 96.92197
## 2901 11 96.92197
## 2902 11 96.92197
## 2903 11 96.92197
## 2904 11 96.92197
## 2905 9 149.85701
## 2906 9 149.85701
## 2907 9 149.85701
## 2908 9 149.85701
## 2909 9 149.85701
## 2910 9 149.85701
## 2911 9 149.85701
## 2912 9 149.85701
## 2913 9 149.85701
## 2914 9 149.85701
## 2915 9 149.85701
## 2916 9 149.85701
## 2917 9 149.85701
## 2918 9 149.85701
## 2919 9 149.85701
## 2920 9 149.85701
## 2921 9 149.85701
## 2922 9 149.85701
## 2923 9 149.85701
## 2924 9 149.85701
## 2925 9 149.85701
## 2926 9 149.85701
## 2927 9 149.85701
## 2928 9 149.85701
## 2929 10 158.73461
## 2930 10 158.73461
## 2931 10 158.73461
## 2932 10 158.73461
## 2933 10 158.73461
## 2934 10 158.73461
## 2935 10 158.73461
## 2936 10 158.73461
## 2937 10 158.73461
## 2938 10 158.73461
## 2939 10 158.73461
## 2940 10 158.73461
## 2941 10 158.73461
## 2942 10 158.73461
## 2943 10 158.73461
## 2944 10 158.73461
## 2945 10 158.73461
## 2946 10 158.73461
## 2947 10 158.73461
## 2948 10 158.73461
## 2949 10 158.73461
## 2950 10 158.73461
## 2951 10 158.73461
## 2952 10 158.73461
## 2953 8 185.82102
## 2954 8 185.82102
## 2955 8 185.82102
## 2956 8 185.82102
## 2957 8 185.82102
## 2958 8 185.82102
## 2959 8 185.82102
## 2960 8 185.82102
## 2961 8 185.82102
## 2962 8 185.82102
## 2963 8 185.82102
## 2964 8 185.82102
## 2965 8 185.82102
## 2966 8 185.82102
## 2967 8 185.82102
## 2968 8 185.82102
## 2969 8 185.82102
## 2970 8 185.82102
## 2971 8 185.82102
## 2972 8 185.82102
## 2973 8 185.82102
## 2974 8 185.82102
## 2975 8 185.82102
## 2976 8 185.82102
## 2977 8 134.71835
## 2978 8 134.71835
## 2979 8 134.71835
## 2980 8 134.71835
## 2981 8 134.71835
## 2982 8 134.71835
## 2983 8 134.71835
## 2984 8 134.71835
## 2985 8 134.71835
## 2986 8 134.71835
## 2987 8 134.71835
## 2988 8 134.71835
## 2989 8 134.71835
## 2990 8 134.71835
## 2991 8 134.71835
## 2992 8 134.71835
## 2993 8 134.71835
## 2994 8 134.71835
## 2995 8 134.71835
## 2996 8 134.71835
## 2997 8 134.71835
## 2998 8 134.71835
## 2999 8 134.71835
## 3000 8 134.71835
## 3001 6 117.16941
## 3002 6 117.16941
## 3003 6 117.16941
## 3004 6 117.16941
## 3005 6 117.16941
## 3006 6 117.16941
## 3007 6 117.16941
## 3008 6 117.16941
## 3009 6 117.16941
## 3010 6 117.16941
## 3011 6 117.16941
## 3012 6 117.16941
## 3013 6 117.16941
## 3014 6 117.16941
## 3015 6 117.16941
## 3016 6 117.16941
## 3017 6 117.16941
## 3018 6 117.16941
## 3019 6 117.16941
## 3020 6 117.16941
## 3021 6 117.16941
## 3022 6 117.16941
## 3023 6 117.16941
## 3024 6 117.16941
## 3025 8 102.14115
## 3026 8 102.14115
## 3027 8 102.14115
## 3028 8 102.14115
## 3029 8 102.14115
## 3030 8 102.14115
## 3031 8 102.14115
## 3032 8 102.14115
## 3033 8 102.14115
## 3034 8 102.14115
## 3035 8 102.14115
## 3036 8 102.14115
## 3037 8 102.14115
## 3038 8 102.14115
## 3039 8 102.14115
## 3040 8 102.14115
## 3041 8 102.14115
## 3042 8 102.14115
## 3043 8 102.14115
## 3044 8 102.14115
## 3045 8 102.14115
## 3046 8 102.14115
## 3047 8 102.14115
## 3048 8 102.14115
## 3049 9 93.17670
## 3050 9 93.17670
## 3051 9 93.17670
## 3052 9 93.17670
## 3053 9 93.17670
## 3054 9 93.17670
## 3055 9 93.17670
## 3056 9 93.17670
## 3057 9 93.17670
## 3058 9 93.17670
## 3059 9 93.17670
## 3060 9 93.17670
## 3061 9 93.17670
## 3062 9 93.17670
## 3063 9 93.17670
## 3064 9 93.17670
## 3065 9 93.17670
## 3066 9 93.17670
## 3067 9 93.17670
## 3068 9 93.17670
## 3069 9 93.17670
## 3070 9 93.17670
## 3071 9 93.17670
## 3072 9 93.17670
## 3073 11 96.92197
## 3074 11 96.92197
## 3075 11 96.92197
## 3076 11 96.92197
## 3077 11 96.92197
## 3078 11 96.92197
## 3079 11 96.92197
## 3080 11 96.92197
## 3081 11 96.92197
## 3082 11 96.92197
## 3083 11 96.92197
## 3084 11 96.92197
## 3085 11 96.92197
## 3086 11 96.92197
## 3087 11 96.92197
## 3088 11 96.92197
## 3089 11 96.92197
## 3090 11 96.92197
## 3091 11 96.92197
## 3092 11 96.92197
## 3093 11 96.92197
## 3094 11 96.92197
## 3095 11 96.92197
## 3096 11 96.92197
## 3097 10 226.72885
## 3098 10 226.72885
## 3099 10 226.72885
## 3100 10 226.72885
## 3101 10 226.72885
## 3102 10 226.72885
## 3103 10 226.72885
## 3104 10 226.72885
## 3105 10 226.72885
## 3106 10 226.72885
## 3107 10 226.72885
## 3108 10 226.72885
## 3109 10 226.72885
## 3110 10 226.72885
## 3111 10 226.72885
## 3112 10 226.72885
## 3113 10 226.72885
## 3114 10 226.72885
## 3115 10 226.72885
## 3116 10 226.72885
## 3117 10 226.72885
## 3118 10 226.72885
## 3119 10 226.72885
## 3120 10 226.72885
## 3121 8 128.89784
## 3122 8 128.89784
## 3123 8 128.89784
## 3124 8 128.89784
## 3125 8 128.89784
## 3126 8 128.89784
## 3127 8 128.89784
## 3128 8 128.89784
## 3129 8 128.89784
## 3130 8 128.89784
## 3131 8 128.89784
## 3132 8 128.89784
## 3133 8 128.89784
## 3134 8 128.89784
## 3135 8 128.89784
## 3136 8 128.89784
## 3137 8 128.89784
## 3138 8 128.89784
## 3139 8 128.89784
## 3140 8 128.89784
## 3141 8 128.89784
## 3142 8 128.89784
## 3143 8 128.89784
## 3144 8 128.89784
## 3145 8 213.14406
## 3146 8 213.14406
## 3147 8 213.14406
## 3148 8 213.14406
## 3149 8 213.14406
## 3150 8 213.14406
## 3151 8 213.14406
## 3152 8 213.14406
## 3153 8 213.14406
## 3154 8 213.14406
## 3155 8 213.14406
## 3156 8 213.14406
## 3157 8 213.14406
## 3158 8 213.14406
## 3159 8 213.14406
## 3160 8 213.14406
## 3161 8 213.14406
## 3162 8 213.14406
## 3163 8 213.14406
## 3164 8 213.14406
## 3165 8 213.14406
## 3166 8 213.14406
## 3167 8 213.14406
## 3168 8 213.14406
## 3169 6 171.38523
## 3170 6 171.38523
## 3171 6 171.38523
## 3172 6 171.38523
## 3173 6 171.38523
## 3174 6 171.38523
## 3175 6 171.38523
## 3176 6 171.38523
## 3177 6 171.38523
## 3178 6 171.38523
## 3179 6 171.38523
## 3180 6 171.38523
## 3181 6 171.38523
## 3182 6 171.38523
## 3183 6 171.38523
## 3184 6 171.38523
## 3185 6 171.38523
## 3186 6 171.38523
## 3187 6 171.38523
## 3188 6 171.38523
## 3189 6 171.38523
## 3190 6 171.38523
## 3191 6 171.38523
## 3192 6 171.38523
## 3193 8 119.30850
## 3194 8 119.30850
## 3195 8 119.30850
## 3196 8 119.30850
## 3197 8 119.30850
## 3198 8 119.30850
## 3199 8 119.30850
## 3200 8 119.30850
## 3201 8 119.30850
## 3202 8 119.30850
## 3203 8 119.30850
## 3204 8 119.30850
## 3205 8 119.30850
## 3206 8 119.30850
## 3207 8 119.30850
## 3208 8 119.30850
## 3209 8 119.30850
## 3210 8 119.30850
## 3211 8 119.30850
## 3212 8 119.30850
## 3213 8 119.30850
## 3214 8 119.30850
## 3215 8 119.30850
## 3216 8 119.30850
## 3217 7 103.92120
## 3218 7 103.92120
## 3219 7 103.92120
## 3220 7 103.92120
## 3221 7 103.92120
## 3222 7 103.92120
## 3223 7 103.92120
## 3224 7 103.92120
## 3225 7 103.92120
## total_metaecosystem_Ble_indiv total_metaecosystem_Cep_indiv
## 1 217.1512 1794.767
## 2 217.1512 1794.767
## 3 217.1512 1794.767
## 4 217.1512 1794.767
## 5 217.1512 1794.767
## 6 217.1512 1794.767
## 7 217.1512 1794.767
## 8 217.1512 1794.767
## 9 217.1512 1794.767
## 10 217.1512 1794.767
## 11 217.1512 1794.767
## 12 217.1512 1794.767
## 13 217.1512 1794.767
## 14 217.1512 1794.767
## 15 217.1512 1794.767
## 16 217.1512 1794.767
## 17 217.1512 1794.767
## 18 217.1512 1794.767
## 19 217.1512 1794.767
## 20 217.1512 1794.767
## 21 217.1512 1794.767
## 22 217.1512 1794.767
## 23 217.1512 1794.767
## 24 217.1512 1794.767
## 25 1037.7907 8056.395
## 26 1037.7907 8056.395
## 27 1037.7907 8056.395
## 28 1037.7907 8056.395
## 29 1037.7907 8056.395
## 30 1037.7907 8056.395
## 31 1037.7907 8056.395
## 32 1037.7907 8056.395
## 33 1037.7907 8056.395
## 34 1037.7907 8056.395
## 35 1037.7907 8056.395
## 36 1037.7907 8056.395
## 37 1037.7907 8056.395
## 38 1037.7907 8056.395
## 39 1037.7907 8056.395
## 40 1037.7907 8056.395
## 41 1037.7907 8056.395
## 42 1037.7907 8056.395
## 43 1037.7907 8056.395
## 44 1037.7907 8056.395
## 45 1037.7907 8056.395
## 46 1037.7907 8056.395
## 47 1037.7907 8056.395
## 48 1037.7907 8056.395
## 49 2398.2558 11759.302
## 50 2398.2558 11759.302
## 51 2398.2558 11759.302
## 52 2398.2558 11759.302
## 53 2398.2558 11759.302
## 54 2398.2558 11759.302
## 55 2398.2558 11759.302
## 56 2398.2558 11759.302
## 57 2398.2558 11759.302
## 58 2398.2558 11759.302
## 59 2398.2558 11759.302
## 60 2398.2558 11759.302
## 61 2398.2558 11759.302
## 62 2398.2558 11759.302
## 63 2398.2558 11759.302
## 64 2398.2558 11759.302
## 65 2398.2558 11759.302
## 66 2398.2558 11759.302
## 67 2398.2558 11759.302
## 68 2398.2558 11759.302
## 69 2398.2558 11759.302
## 70 2398.2558 11759.302
## 71 2398.2558 11759.302
## 72 2398.2558 11759.302
## 73 3174.4186 6552.907
## 74 3174.4186 6552.907
## 75 3174.4186 6552.907
## 76 3174.4186 6552.907
## 77 3174.4186 6552.907
## 78 3174.4186 6552.907
## 79 3174.4186 6552.907
## 80 3174.4186 6552.907
## 81 3174.4186 6552.907
## 82 3174.4186 6552.907
## 83 3174.4186 6552.907
## 84 3174.4186 6552.907
## 85 3174.4186 6552.907
## 86 3174.4186 6552.907
## 87 3174.4186 6552.907
## 88 3174.4186 6552.907
## 89 3174.4186 6552.907
## 90 3174.4186 6552.907
## 91 3174.4186 6552.907
## 92 3174.4186 6552.907
## 93 3174.4186 6552.907
## 94 3174.4186 6552.907
## 95 3174.4186 6552.907
## 96 3174.4186 6552.907
## 97 4006.3953 9326.163
## 98 4006.3953 9326.163
## 99 4006.3953 9326.163
## 100 4006.3953 9326.163
## 101 4006.3953 9326.163
## 102 4006.3953 9326.163
## 103 4006.3953 9326.163
## 104 4006.3953 9326.163
## 105 4006.3953 9326.163
## 106 4006.3953 9326.163
## 107 4006.3953 9326.163
## 108 4006.3953 9326.163
## 109 4006.3953 9326.163
## 110 4006.3953 9326.163
## 111 4006.3953 9326.163
## 112 4006.3953 9326.163
## 113 4006.3953 9326.163
## 114 4006.3953 9326.163
## 115 4006.3953 9326.163
## 116 4006.3953 9326.163
## 117 4006.3953 9326.163
## 118 4006.3953 9326.163
## 119 4006.3953 9326.163
## 120 4006.3953 9326.163
## 121 3750.0000 9818.023
## 122 3750.0000 9818.023
## 123 3750.0000 9818.023
## 124 3750.0000 9818.023
## 125 3750.0000 9818.023
## 126 3750.0000 9818.023
## 127 3750.0000 9818.023
## 128 3750.0000 9818.023
## 129 3750.0000 9818.023
## 130 3750.0000 9818.023
## 131 3750.0000 9818.023
## 132 3750.0000 9818.023
## 133 3750.0000 9818.023
## 134 3750.0000 9818.023
## 135 3750.0000 9818.023
## 136 3750.0000 9818.023
## 137 3750.0000 9818.023
## 138 3750.0000 9818.023
## 139 3750.0000 9818.023
## 140 3750.0000 9818.023
## 141 3750.0000 9818.023
## 142 3750.0000 9818.023
## 143 3750.0000 9818.023
## 144 3750.0000 9818.023
## 145 2986.9186 15800.581
## 146 2986.9186 15800.581
## 147 2986.9186 15800.581
## 148 2986.9186 15800.581
## 149 2986.9186 15800.581
## 150 2986.9186 15800.581
## 151 2986.9186 15800.581
## 152 2986.9186 15800.581
## 153 2986.9186 15800.581
## 154 2986.9186 15800.581
## 155 2986.9186 15800.581
## 156 2986.9186 15800.581
## 157 2986.9186 15800.581
## 158 2986.9186 15800.581
## 159 2986.9186 15800.581
## 160 2986.9186 15800.581
## 161 2986.9186 15800.581
## 162 2986.9186 15800.581
## 163 2986.9186 15800.581
## 164 2986.9186 15800.581
## 165 2986.9186 15800.581
## 166 2986.9186 15800.581
## 167 2986.9186 15800.581
## 168 2986.9186 15800.581
## 169 1748.5465 15422.093
## 170 1748.5465 15422.093
## 171 1748.5465 15422.093
## 172 1748.5465 15422.093
## 173 1748.5465 15422.093
## 174 1748.5465 15422.093
## 175 1748.5465 15422.093
## 176 1748.5465 15422.093
## 177 1748.5465 15422.093
## 178 1748.5465 15422.093
## 179 1748.5465 15422.093
## 180 1748.5465 15422.093
## 181 1748.5465 15422.093
## 182 1748.5465 15422.093
## 183 1748.5465 15422.093
## 184 1748.5465 15422.093
## 185 1748.5465 15422.093
## 186 1748.5465 15422.093
## 187 1748.5465 15422.093
## 188 1748.5465 15422.093
## 189 1748.5465 15422.093
## 190 1748.5465 15422.093
## 191 1748.5465 15422.093
## 192 1748.5465 15422.093
## 193 217.1512 1794.767
## 194 217.1512 1794.767
## 195 217.1512 1794.767
## 196 217.1512 1794.767
## 197 217.1512 1794.767
## 198 217.1512 1794.767
## 199 217.1512 1794.767
## 200 217.1512 1794.767
## 201 217.1512 1794.767
## 202 217.1512 1794.767
## 203 217.1512 1794.767
## 204 217.1512 1794.767
## 205 217.1512 1794.767
## 206 217.1512 1794.767
## 207 217.1512 1794.767
## 208 217.1512 1794.767
## 209 217.1512 1794.767
## 210 217.1512 1794.767
## 211 217.1512 1794.767
## 212 217.1512 1794.767
## 213 217.1512 1794.767
## 214 217.1512 1794.767
## 215 217.1512 1794.767
## 216 217.1512 1794.767
## 217 5537.7907 9695.930
## 218 5537.7907 9695.930
## 219 5537.7907 9695.930
## 220 5537.7907 9695.930
## 221 5537.7907 9695.930
## 222 5537.7907 9695.930
## 223 5537.7907 9695.930
## 224 5537.7907 9695.930
## 225 5537.7907 9695.930
## 226 5537.7907 9695.930
## 227 5537.7907 9695.930
## 228 5537.7907 9695.930
## 229 5537.7907 9695.930
## 230 5537.7907 9695.930
## 231 5537.7907 9695.930
## 232 5537.7907 9695.930
## 233 5537.7907 9695.930
## 234 5537.7907 9695.930
## 235 5537.7907 9695.930
## 236 5537.7907 9695.930
## 237 5537.7907 9695.930
## 238 5537.7907 9695.930
## 239 5537.7907 9695.930
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## 851 2398.2558 8680.814
## 852 2398.2558 8680.814
## 853 2398.2558 8680.814
## 854 2398.2558 8680.814
## 855 2398.2558 8680.814
## 856 2398.2558 8680.814
## 857 2398.2558 8680.814
## 858 2398.2558 8680.814
## 859 2398.2558 8680.814
## 860 2398.2558 8680.814
## 861 2398.2558 8680.814
## 862 2398.2558 8680.814
## 863 2398.2558 8680.814
## 864 2398.2558 8680.814
## 865 1512.2093 13041.279
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## 869 1512.2093 13041.279
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## 879 1512.2093 13041.279
## 880 1512.2093 13041.279
## 881 1512.2093 13041.279
## 882 1512.2093 13041.279
## 883 1512.2093 13041.279
## 884 1512.2093 13041.279
## 885 1512.2093 13041.279
## 886 1512.2093 13041.279
## 887 1512.2093 13041.279
## 888 1512.2093 13041.279
## 889 2162.7907 8448.837
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## 891 2162.7907 8448.837
## 892 2162.7907 8448.837
## 893 2162.7907 8448.837
## 894 2162.7907 8448.837
## 895 2162.7907 8448.837
## 896 2162.7907 8448.837
## 897 2162.7907 8448.837
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## 899 2162.7907 8448.837
## 900 2162.7907 8448.837
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## 902 2162.7907 8448.837
## 903 2162.7907 8448.837
## 904 2162.7907 8448.837
## 905 2162.7907 8448.837
## 906 2162.7907 8448.837
## 907 2162.7907 8448.837
## 908 2162.7907 8448.837
## 909 2162.7907 8448.837
## 910 2162.7907 8448.837
## 911 2162.7907 8448.837
## 912 2162.7907 8448.837
## 913 4547.9651 9857.267
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## 915 4547.9651 9857.267
## 916 4547.9651 9857.267
## 917 4547.9651 9857.267
## 918 4547.9651 9857.267
## 919 4547.9651 9857.267
## 920 4547.9651 9857.267
## 921 4547.9651 9857.267
## 922 4547.9651 9857.267
## 923 4547.9651 9857.267
## 924 4547.9651 9857.267
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## 927 4547.9651 9857.267
## 928 4547.9651 9857.267
## 929 4547.9651 9857.267
## 930 4547.9651 9857.267
## 931 4547.9651 9857.267
## 932 4547.9651 9857.267
## 933 4547.9651 9857.267
## 934 4547.9651 9857.267
## 935 4547.9651 9857.267
## 936 4547.9651 9857.267
## 937 3920.0581 16067.442
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## 941 3920.0581 16067.442
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## 958 3920.0581 16067.442
## 959 3920.0581 16067.442
## 960 3920.0581 16067.442
## 961 217.1512 1794.767
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## 1198 5319.7674 8802.907
## 1199 5319.7674 8802.907
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## 1436 4709.3023 8307.558
## 1437 4709.3023 8307.558
## 1438 4709.3023 8307.558
## 1439 4709.3023 8307.558
## 1440 4709.3023 8307.558
## 1441 5345.9302 10449.419
## 1442 5345.9302 10449.419
## 1443 5345.9302 10449.419
## 1444 5345.9302 10449.419
## 1445 5345.9302 10449.419
## 1446 5345.9302 10449.419
## 1447 5345.9302 10449.419
## 1448 5345.9302 10449.419
## 1449 5345.9302 10449.419
## 1450 5345.9302 10449.419
## 1451 5345.9302 10449.419
## 1452 5345.9302 10449.419
## 1453 5345.9302 10449.419
## 1454 5345.9302 10449.419
## 1455 5345.9302 10449.419
## 1456 5345.9302 10449.419
## 1457 5345.9302 10449.419
## 1458 5345.9302 10449.419
## 1459 5345.9302 10449.419
## 1460 5345.9302 10449.419
## 1461 5345.9302 10449.419
## 1462 5345.9302 10449.419
## 1463 5345.9302 10449.419
## 1464 5345.9302 10449.419
## 1465 7709.3023 3279.070
## 1466 7709.3023 3279.070
## 1467 7709.3023 3279.070
## 1468 7709.3023 3279.070
## 1469 7709.3023 3279.070
## 1470 7709.3023 3279.070
## 1471 7709.3023 3279.070
## 1472 7709.3023 3279.070
## 1473 7709.3023 3279.070
## 1474 7709.3023 3279.070
## 1475 7709.3023 3279.070
## 1476 7709.3023 3279.070
## 1477 7709.3023 3279.070
## 1478 7709.3023 3279.070
## 1479 7709.3023 3279.070
## 1480 7709.3023 3279.070
## 1481 7709.3023 3279.070
## 1482 7709.3023 3279.070
## 1483 7709.3023 3279.070
## 1484 7709.3023 3279.070
## 1485 7709.3023 3279.070
## 1486 7709.3023 3279.070
## 1487 7709.3023 3279.070
## 1488 7709.3023 3279.070
## 1489 3553.7791 13829.651
## 1490 3553.7791 13829.651
## 1491 3553.7791 13829.651
## 1492 3553.7791 13829.651
## 1493 3553.7791 13829.651
## 1494 3553.7791 13829.651
## 1495 3553.7791 13829.651
## 1496 3553.7791 13829.651
## 1497 3553.7791 13829.651
## 1498 3553.7791 13829.651
## 1499 3553.7791 13829.651
## 1500 3553.7791 13829.651
## 1501 3553.7791 13829.651
## 1502 3553.7791 13829.651
## 1503 3553.7791 13829.651
## 1504 3553.7791 13829.651
## 1505 3553.7791 13829.651
## 1506 3553.7791 13829.651
## 1507 3553.7791 13829.651
## 1508 3553.7791 13829.651
## 1509 3553.7791 13829.651
## 1510 3553.7791 13829.651
## 1511 3553.7791 13829.651
## 1512 3553.7791 13829.651
## 1513 2180.2326 19895.930
## 1514 2180.2326 19895.930
## 1515 2180.2326 19895.930
## 1516 2180.2326 19895.930
## 1517 2180.2326 19895.930
## 1518 2180.2326 19895.930
## 1519 2180.2326 19895.930
## 1520 2180.2326 19895.930
## 1521 2180.2326 19895.930
## 1522 2180.2326 19895.930
## 1523 2180.2326 19895.930
## 1524 2180.2326 19895.930
## 1525 2180.2326 19895.930
## 1526 2180.2326 19895.930
## 1527 2180.2326 19895.930
## 1528 2180.2326 19895.930
## 1529 2180.2326 19895.930
## 1530 2180.2326 19895.930
## 1531 2180.2326 19895.930
## 1532 2180.2326 19895.930
## 1533 2180.2326 19895.930
## 1534 2180.2326 19895.930
## 1535 2180.2326 19895.930
## 1536 2180.2326 19895.930
## 1537 217.1512 1794.767
## 1538 217.1512 1794.767
## 1539 217.1512 1794.767
## 1540 217.1512 1794.767
## 1541 217.1512 1794.767
## 1542 217.1512 1794.767
## 1543 217.1512 1794.767
## 1544 217.1512 1794.767
## 1545 217.1512 1794.767
## 1546 217.1512 1794.767
## 1547 217.1512 1794.767
## 1548 217.1512 1794.767
## 1549 217.1512 1794.767
## 1550 217.1512 1794.767
## 1551 217.1512 1794.767
## 1552 217.1512 1794.767
## 1553 217.1512 1794.767
## 1554 217.1512 1794.767
## 1555 217.1512 1794.767
## 1556 217.1512 1794.767
## 1557 217.1512 1794.767
## 1558 217.1512 1794.767
## 1559 217.1512 1794.767
## 1560 217.1512 1794.767
## 1561 1090.1163 9334.884
## 1562 1090.1163 9334.884
## 1563 1090.1163 9334.884
## 1564 1090.1163 9334.884
## 1565 1090.1163 9334.884
## 1566 1090.1163 9334.884
## 1567 1090.1163 9334.884
## 1568 1090.1163 9334.884
## 1569 1090.1163 9334.884
## 1570 1090.1163 9334.884
## 1571 1090.1163 9334.884
## 1572 1090.1163 9334.884
## 1573 1090.1163 9334.884
## 1574 1090.1163 9334.884
## 1575 1090.1163 9334.884
## 1576 1090.1163 9334.884
## 1577 1090.1163 9334.884
## 1578 1090.1163 9334.884
## 1579 1090.1163 9334.884
## 1580 1090.1163 9334.884
## 1581 1090.1163 9334.884
## 1582 1090.1163 9334.884
## 1583 1090.1163 9334.884
## 1584 1090.1163 9334.884
## 1585 1796.5116 20522.093
## 1586 1796.5116 20522.093
## 1587 1796.5116 20522.093
## 1588 1796.5116 20522.093
## 1589 1796.5116 20522.093
## 1590 1796.5116 20522.093
## 1591 1796.5116 20522.093
## 1592 1796.5116 20522.093
## 1593 1796.5116 20522.093
## 1594 1796.5116 20522.093
## 1595 1796.5116 20522.093
## 1596 1796.5116 20522.093
## 1597 1796.5116 20522.093
## 1598 1796.5116 20522.093
## 1599 1796.5116 20522.093
## 1600 1796.5116 20522.093
## 1601 1796.5116 20522.093
## 1602 1796.5116 20522.093
## 1603 1796.5116 20522.093
## 1604 1796.5116 20522.093
## 1605 1796.5116 20522.093
## 1606 1796.5116 20522.093
## 1607 1796.5116 20522.093
## 1608 1796.5116 20522.093
## 1609 2616.2791 11761.047
## 1610 2616.2791 11761.047
## 1611 2616.2791 11761.047
## 1612 2616.2791 11761.047
## 1613 2616.2791 11761.047
## 1614 2616.2791 11761.047
## 1615 2616.2791 11761.047
## 1616 2616.2791 11761.047
## 1617 2616.2791 11761.047
## 1618 2616.2791 11761.047
## 1619 2616.2791 11761.047
## 1620 2616.2791 11761.047
## 1621 2616.2791 11761.047
## 1622 2616.2791 11761.047
## 1623 2616.2791 11761.047
## 1624 2616.2791 11761.047
## 1625 2616.2791 11761.047
## 1626 2616.2791 11761.047
## 1627 2616.2791 11761.047
## 1628 2616.2791 11761.047
## 1629 2616.2791 11761.047
## 1630 2616.2791 11761.047
## 1631 2616.2791 11761.047
## 1632 2616.2791 11761.047
## 1633 3680.2326 10379.651
## 1634 3680.2326 10379.651
## 1635 3680.2326 10379.651
## 1636 3680.2326 10379.651
## 1637 3680.2326 10379.651
## 1638 3680.2326 10379.651
## 1639 3680.2326 10379.651
## 1640 3680.2326 10379.651
## 1641 3680.2326 10379.651
## 1642 3680.2326 10379.651
## 1643 3680.2326 10379.651
## 1644 3680.2326 10379.651
## 1645 3680.2326 10379.651
## 1646 3680.2326 10379.651
## 1647 3680.2326 10379.651
## 1648 3680.2326 10379.651
## 1649 3680.2326 10379.651
## 1650 3680.2326 10379.651
## 1651 3680.2326 10379.651
## 1652 3680.2326 10379.651
## 1653 3680.2326 10379.651
## 1654 3680.2326 10379.651
## 1655 3680.2326 10379.651
## 1656 3680.2326 10379.651
## 1657 4360.4651 4901.163
## 1658 4360.4651 4901.163
## 1659 4360.4651 4901.163
## 1660 4360.4651 4901.163
## 1661 4360.4651 4901.163
## 1662 4360.4651 4901.163
## 1663 4360.4651 4901.163
## 1664 4360.4651 4901.163
## 1665 4360.4651 4901.163
## 1666 4360.4651 4901.163
## 1667 4360.4651 4901.163
## 1668 4360.4651 4901.163
## 1669 4360.4651 4901.163
## 1670 4360.4651 4901.163
## 1671 4360.4651 4901.163
## 1672 4360.4651 4901.163
## 1673 4360.4651 4901.163
## 1674 4360.4651 4901.163
## 1675 4360.4651 4901.163
## 1676 4360.4651 4901.163
## 1677 4360.4651 4901.163
## 1678 4360.4651 4901.163
## 1679 4360.4651 4901.163
## 1680 4360.4651 4901.163
## 1681 1090.1163 4332.558
## 1682 1090.1163 4332.558
## 1683 1090.1163 4332.558
## 1684 1090.1163 4332.558
## 1685 1090.1163 4332.558
## 1686 1090.1163 4332.558
## 1687 1090.1163 4332.558
## 1688 1090.1163 4332.558
## 1689 1090.1163 4332.558
## 1690 1090.1163 4332.558
## 1691 1090.1163 4332.558
## 1692 1090.1163 4332.558
## 1693 1090.1163 4332.558
## 1694 1090.1163 4332.558
## 1695 1090.1163 4332.558
## 1696 1090.1163 4332.558
## 1697 1090.1163 4332.558
## 1698 1090.1163 4332.558
## 1699 1090.1163 4332.558
## 1700 1090.1163 4332.558
## 1701 1090.1163 4332.558
## 1702 1090.1163 4332.558
## 1703 1090.1163 4332.558
## 1704 1090.1163 4332.558
## 1705 2180.2326 2048.547
## 1706 2180.2326 2048.547
## 1707 2180.2326 2048.547
## 1708 2180.2326 2048.547
## 1709 2180.2326 2048.547
## 1710 2180.2326 2048.547
## 1711 2180.2326 2048.547
## 1712 2180.2326 2048.547
## 1713 2180.2326 2048.547
## 1714 2180.2326 2048.547
## 1715 2180.2326 2048.547
## 1716 2180.2326 2048.547
## 1717 2180.2326 2048.547
## 1718 2180.2326 2048.547
## 1719 2180.2326 2048.547
## 1720 2180.2326 2048.547
## 1721 2180.2326 2048.547
## 1722 2180.2326 2048.547
## 1723 2180.2326 2048.547
## 1724 2180.2326 2048.547
## 1725 2180.2326 2048.547
## 1726 2180.2326 2048.547
## 1727 2180.2326 2048.547
## 1728 2180.2326 2048.547
## 1729 217.1512 1794.767
## 1730 217.1512 1794.767
## 1731 217.1512 1794.767
## 1732 217.1512 1794.767
## 1733 217.1512 1794.767
## 1734 217.1512 1794.767
## 1735 217.1512 1794.767
## 1736 217.1512 1794.767
## 1737 217.1512 1794.767
## 1738 217.1512 1794.767
## 1739 217.1512 1794.767
## 1740 217.1512 1794.767
## 1741 217.1512 1794.767
## 1742 217.1512 1794.767
## 1743 217.1512 1794.767
## 1744 217.1512 1794.767
## 1745 217.1512 1794.767
## 1746 217.1512 1794.767
## 1747 217.1512 1794.767
## 1748 217.1512 1794.767
## 1749 217.1512 1794.767
## 1750 217.1512 1794.767
## 1751 217.1512 1794.767
## 1752 217.1512 1794.767
## 1753 1090.1163 7660.465
## 1754 1090.1163 7660.465
## 1755 1090.1163 7660.465
## 1756 1090.1163 7660.465
## 1757 1090.1163 7660.465
## 1758 1090.1163 7660.465
## 1759 1090.1163 7660.465
## 1760 1090.1163 7660.465
## 1761 1090.1163 7660.465
## 1762 1090.1163 7660.465
## 1763 1090.1163 7660.465
## 1764 1090.1163 7660.465
## 1765 1090.1163 7660.465
## 1766 1090.1163 7660.465
## 1767 1090.1163 7660.465
## 1768 1090.1163 7660.465
## 1769 1090.1163 7660.465
## 1770 1090.1163 7660.465
## 1771 1090.1163 7660.465
## 1772 1090.1163 7660.465
## 1773 1090.1163 7660.465
## 1774 1090.1163 7660.465
## 1775 1090.1163 7660.465
## 1776 1090.1163 7660.465
## 1777 2886.6279 13658.721
## 1778 2886.6279 13658.721
## 1779 2886.6279 13658.721
## 1780 2886.6279 13658.721
## 1781 2886.6279 13658.721
## 1782 2886.6279 13658.721
## 1783 2886.6279 13658.721
## 1784 2886.6279 13658.721
## 1785 2886.6279 13658.721
## 1786 2886.6279 13658.721
## 1787 2886.6279 13658.721
## 1788 2886.6279 13658.721
## 1789 2886.6279 13658.721
## 1790 2886.6279 13658.721
## 1791 2886.6279 13658.721
## 1792 2886.6279 13658.721
## 1793 2886.6279 13658.721
## 1794 2886.6279 13658.721
## 1795 2886.6279 13658.721
## 1796 2886.6279 13658.721
## 1797 2886.6279 13658.721
## 1798 2886.6279 13658.721
## 1799 2886.6279 13658.721
## 1800 2886.6279 13658.721
## 1801 2616.2791 10217.442
## 1802 2616.2791 10217.442
## 1803 2616.2791 10217.442
## 1804 2616.2791 10217.442
## 1805 2616.2791 10217.442
## 1806 2616.2791 10217.442
## 1807 2616.2791 10217.442
## 1808 2616.2791 10217.442
## 1809 2616.2791 10217.442
## 1810 2616.2791 10217.442
## 1811 2616.2791 10217.442
## 1812 2616.2791 10217.442
## 1813 2616.2791 10217.442
## 1814 2616.2791 10217.442
## 1815 2616.2791 10217.442
## 1816 2616.2791 10217.442
## 1817 2616.2791 10217.442
## 1818 2616.2791 10217.442
## 1819 2616.2791 10217.442
## 1820 2616.2791 10217.442
## 1821 2616.2791 10217.442
## 1822 2616.2791 10217.442
## 1823 2616.2791 10217.442
## 1824 2616.2791 10217.442
## 1825 1090.1163 12760.465
## 1826 1090.1163 12760.465
## 1827 1090.1163 12760.465
## 1828 1090.1163 12760.465
## 1829 1090.1163 12760.465
## 1830 1090.1163 12760.465
## 1831 1090.1163 12760.465
## 1832 1090.1163 12760.465
## 1833 1090.1163 12760.465
## 1834 1090.1163 12760.465
## 1835 1090.1163 12760.465
## 1836 1090.1163 12760.465
## 1837 1090.1163 12760.465
## 1838 1090.1163 12760.465
## 1839 1090.1163 12760.465
## 1840 1090.1163 12760.465
## 1841 1090.1163 12760.465
## 1842 1090.1163 12760.465
## 1843 1090.1163 12760.465
## 1844 1090.1163 12760.465
## 1845 1090.1163 12760.465
## 1846 1090.1163 12760.465
## 1847 1090.1163 12760.465
## 1848 1090.1163 12760.465
## 1849 2162.7907 8005.814
## 1850 2162.7907 8005.814
## 1851 2162.7907 8005.814
## 1852 2162.7907 8005.814
## 1853 2162.7907 8005.814
## 1854 2162.7907 8005.814
## 1855 2162.7907 8005.814
## 1856 2162.7907 8005.814
## 1857 2162.7907 8005.814
## 1858 2162.7907 8005.814
## 1859 2162.7907 8005.814
## 1860 2162.7907 8005.814
## 1861 2162.7907 8005.814
## 1862 2162.7907 8005.814
## 1863 2162.7907 8005.814
## 1864 2162.7907 8005.814
## 1865 2162.7907 8005.814
## 1866 2162.7907 8005.814
## 1867 2162.7907 8005.814
## 1868 2162.7907 8005.814
## 1869 2162.7907 8005.814
## 1870 2162.7907 8005.814
## 1871 2162.7907 8005.814
## 1872 2162.7907 8005.814
## 1873 4329.9419 9743.895
## 1874 4329.9419 9743.895
## 1875 4329.9419 9743.895
## 1876 4329.9419 9743.895
## 1877 4329.9419 9743.895
## 1878 4329.9419 9743.895
## 1879 4329.9419 9743.895
## 1880 4329.9419 9743.895
## 1881 4329.9419 9743.895
## 1882 4329.9419 9743.895
## 1883 4329.9419 9743.895
## 1884 4329.9419 9743.895
## 1885 4329.9419 9743.895
## 1886 4329.9419 9743.895
## 1887 4329.9419 9743.895
## 1888 4329.9419 9743.895
## 1889 4329.9419 9743.895
## 1890 4329.9419 9743.895
## 1891 4329.9419 9743.895
## 1892 4329.9419 9743.895
## 1893 4329.9419 9743.895
## 1894 4329.9419 9743.895
## 1895 4329.9419 9743.895
## 1896 4329.9419 9743.895
## 1897 3920.0581 16006.395
## 1898 3920.0581 16006.395
## 1899 3920.0581 16006.395
## 1900 3920.0581 16006.395
## 1901 3920.0581 16006.395
## 1902 3920.0581 16006.395
## 1903 3920.0581 16006.395
## 1904 3920.0581 16006.395
## 1905 3920.0581 16006.395
## 1906 3920.0581 16006.395
## 1907 3920.0581 16006.395
## 1908 3920.0581 16006.395
## 1909 3920.0581 16006.395
## 1910 3920.0581 16006.395
## 1911 3920.0581 16006.395
## 1912 3920.0581 16006.395
## 1913 3920.0581 16006.395
## 1914 3920.0581 16006.395
## 1915 3920.0581 16006.395
## 1916 3920.0581 16006.395
## 1917 3920.0581 16006.395
## 1918 3920.0581 16006.395
## 1919 3920.0581 16006.395
## 1920 3920.0581 16006.395
## 1921 217.1512 1794.767
## 1922 217.1512 1794.767
## 1923 217.1512 1794.767
## 1924 217.1512 1794.767
## 1925 217.1512 1794.767
## 1926 217.1512 1794.767
## 1927 217.1512 1794.767
## 1928 217.1512 1794.767
## 1929 217.1512 1794.767
## 1930 217.1512 1794.767
## 1931 217.1512 1794.767
## 1932 217.1512 1794.767
## 1933 217.1512 1794.767
## 1934 217.1512 1794.767
## 1935 217.1512 1794.767
## 1936 217.1512 1794.767
## 1937 217.1512 1794.767
## 1938 217.1512 1794.767
## 1939 217.1512 1794.767
## 1940 217.1512 1794.767
## 1941 217.1512 1794.767
## 1942 217.1512 1794.767
## 1943 217.1512 1794.767
## 1944 217.1512 1794.767
## 1945 1473.8372 7573.256
## 1946 1473.8372 7573.256
## 1947 1473.8372 7573.256
## 1948 1473.8372 7573.256
## 1949 1473.8372 7573.256
## 1950 1473.8372 7573.256
## 1951 1473.8372 7573.256
## 1952 1473.8372 7573.256
## 1953 1473.8372 7573.256
## 1954 1473.8372 7573.256
## 1955 1473.8372 7573.256
## 1956 1473.8372 7573.256
## 1957 1473.8372 7573.256
## 1958 1473.8372 7573.256
## 1959 1473.8372 7573.256
## 1960 1473.8372 7573.256
## 1961 1473.8372 7573.256
## 1962 1473.8372 7573.256
## 1963 1473.8372 7573.256
## 1964 1473.8372 7573.256
## 1965 1473.8372 7573.256
## 1966 1473.8372 7573.256
## 1967 1473.8372 7573.256
## 1968 1473.8372 7573.256
## 1969 2502.9070 11834.302
## 1970 2502.9070 11834.302
## 1971 2502.9070 11834.302
## 1972 2502.9070 11834.302
## 1973 2502.9070 11834.302
## 1974 2502.9070 11834.302
## 1975 2502.9070 11834.302
## 1976 2502.9070 11834.302
## 1977 2502.9070 11834.302
## 1978 2502.9070 11834.302
## 1979 2502.9070 11834.302
## 1980 2502.9070 11834.302
## 1981 2502.9070 11834.302
## 1982 2502.9070 11834.302
## 1983 2502.9070 11834.302
## 1984 2502.9070 11834.302
## 1985 2502.9070 11834.302
## 1986 2502.9070 11834.302
## 1987 2502.9070 11834.302
## 1988 2502.9070 11834.302
## 1989 2502.9070 11834.302
## 1990 2502.9070 11834.302
## 1991 2502.9070 11834.302
## 1992 2502.9070 11834.302
## 1993 3388.9535 8497.674
## 1994 3388.9535 8497.674
## 1995 3388.9535 8497.674
## 1996 3388.9535 8497.674
## 1997 3388.9535 8497.674
## 1998 3388.9535 8497.674
## 1999 3388.9535 8497.674
## 2000 3388.9535 8497.674
## 2001 3388.9535 8497.674
## 2002 3388.9535 8497.674
## 2003 3388.9535 8497.674
## 2004 3388.9535 8497.674
## 2005 3388.9535 8497.674
## 2006 3388.9535 8497.674
## 2007 3388.9535 8497.674
## 2008 3388.9535 8497.674
## 2009 3388.9535 8497.674
## 2010 3388.9535 8497.674
## 2011 3388.9535 8497.674
## 2012 3388.9535 8497.674
## 2013 3388.9535 8497.674
## 2014 3388.9535 8497.674
## 2015 3388.9535 8497.674
## 2016 3388.9535 8497.674
## 2017 3584.3023 9950.581
## 2018 3584.3023 9950.581
## 2019 3584.3023 9950.581
## 2020 3584.3023 9950.581
## 2021 3584.3023 9950.581
## 2022 3584.3023 9950.581
## 2023 3584.3023 9950.581
## 2024 3584.3023 9950.581
## 2025 3584.3023 9950.581
## 2026 3584.3023 9950.581
## 2027 3584.3023 9950.581
## 2028 3584.3023 9950.581
## 2029 3584.3023 9950.581
## 2030 3584.3023 9950.581
## 2031 3584.3023 9950.581
## 2032 3584.3023 9950.581
## 2033 3584.3023 9950.581
## 2034 3584.3023 9950.581
## 2035 3584.3023 9950.581
## 2036 3584.3023 9950.581
## 2037 3584.3023 9950.581
## 2038 3584.3023 9950.581
## 2039 3584.3023 9950.581
## 2040 3584.3023 9950.581
## 2041 3750.0000 9680.233
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## 2051 3750.0000 9680.233
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## 2054 3750.0000 9680.233
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## 2056 3750.0000 9680.233
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## 2059 3750.0000 9680.233
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## 2065 2768.8953 15496.221
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## 2075 2768.8953 15496.221
## 2076 2768.8953 15496.221
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## 2078 2768.8953 15496.221
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## 2080 2768.8953 15496.221
## 2081 2768.8953 15496.221
## 2082 2768.8953 15496.221
## 2083 2768.8953 15496.221
## 2084 2768.8953 15496.221
## 2085 2768.8953 15496.221
## 2086 2768.8953 15496.221
## 2087 2768.8953 15496.221
## 2088 2768.8953 15496.221
## 2089 1748.5465 15620.930
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## 2091 1748.5465 15620.930
## 2092 1748.5465 15620.930
## 2093 1748.5465 15620.930
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## 2095 1748.5465 15620.930
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## 2110 1748.5465 15620.930
## 2111 1748.5465 15620.930
## 2112 1748.5465 15620.930
## 2113 217.1512 1794.767
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## 2137 5973.8372 9212.791
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## 2161 3008.7209 12723.837
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## 2181 3008.7209 12723.837
## 2182 3008.7209 12723.837
## 2183 3008.7209 12723.837
## 2184 3008.7209 12723.837
## 2185 4967.4419 16817.442
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## 2187 4967.4419 16817.442
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## 2189 4967.4419 16817.442
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## 2194 4967.4419 16817.442
## 2195 4967.4419 16817.442
## 2196 4967.4419 16817.442
## 2197 4967.4419 16817.442
## 2198 4967.4419 16817.442
## 2199 4967.4419 16817.442
## 2200 4967.4419 16817.442
## 2201 4967.4419 16817.442
## 2202 4967.4419 16817.442
## 2203 4967.4419 16817.442
## 2204 4967.4419 16817.442
## 2205 4967.4419 16817.442
## 2206 4967.4419 16817.442
## 2207 4967.4419 16817.442
## 2208 4967.4419 16817.442
## 2209 3008.7209 13630.814
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## 2230 3008.7209 13630.814
## 2231 3008.7209 13630.814
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## 2254 2659.8837 8110.465
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## 2280 4765.9884 12243.314
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## 2301 2376.4535 10636.919
## 2302 2376.4535 10636.919
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## 2304 2376.4535 10636.919
## 2305 217.1512 1794.767
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## 2348 3924.4186 7861.047
## 2349 3924.4186 7861.047
## 2350 3924.4186 7861.047
## 2351 3924.4186 7861.047
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## 2353 3819.7674 12837.209
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## 2371 3819.7674 12837.209
## 2372 3819.7674 12837.209
## 2373 3819.7674 12837.209
## 2374 3819.7674 12837.209
## 2375 3819.7674 12837.209
## 2376 3819.7674 12837.209
## 2377 4705.8140 8715.698
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## 2380 4705.8140 8715.698
## 2381 4705.8140 8715.698
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## 2390 4705.8140 8715.698
## 2391 4705.8140 8715.698
## 2392 4705.8140 8715.698
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## 2398 4705.8140 8715.698
## 2399 4705.8140 8715.698
## 2400 4705.8140 8715.698
## 2401 5345.9302 11354.651
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## 2403 5345.9302 11354.651
## 2404 5345.9302 11354.651
## 2405 5345.9302 11354.651
## 2406 5345.9302 11354.651
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## 2408 5345.9302 11354.651
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## 2410 5345.9302 11354.651
## 2411 5345.9302 11354.651
## 2412 5345.9302 11354.651
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## 2414 5345.9302 11354.651
## 2415 5345.9302 11354.651
## 2416 5345.9302 11354.651
## 2417 5345.9302 11354.651
## 2418 5345.9302 11354.651
## 2419 5345.9302 11354.651
## 2420 5345.9302 11354.651
## 2421 5345.9302 11354.651
## 2422 5345.9302 11354.651
## 2423 5345.9302 11354.651
## 2424 5345.9302 11354.651
## 2425 7709.3023 3584.302
## 2426 7709.3023 3584.302
## 2427 7709.3023 3584.302
## 2428 7709.3023 3584.302
## 2429 7709.3023 3584.302
## 2430 7709.3023 3584.302
## 2431 7709.3023 3584.302
## 2432 7709.3023 3584.302
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## 2436 7709.3023 3584.302
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## 2439 7709.3023 3584.302
## 2440 7709.3023 3584.302
## 2441 7709.3023 3584.302
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## 2444 7709.3023 3584.302
## 2445 7709.3023 3584.302
## 2446 7709.3023 3584.302
## 2447 7709.3023 3584.302
## 2448 7709.3023 3584.302
## 2449 3553.7791 13638.663
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## 2458 3553.7791 13638.663
## 2459 3553.7791 13638.663
## 2460 3553.7791 13638.663
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## 2462 3553.7791 13638.663
## 2463 3553.7791 13638.663
## 2464 3553.7791 13638.663
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## 2466 3553.7791 13638.663
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## 2468 3553.7791 13638.663
## 2469 3553.7791 13638.663
## 2470 3553.7791 13638.663
## 2471 3553.7791 13638.663
## 2472 3553.7791 13638.663
## 2473 2180.2326 20155.814
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## 2476 2180.2326 20155.814
## 2477 2180.2326 20155.814
## 2478 2180.2326 20155.814
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## 2480 2180.2326 20155.814
## 2481 2180.2326 20155.814
## 2482 2180.2326 20155.814
## 2483 2180.2326 20155.814
## 2484 2180.2326 20155.814
## 2485 2180.2326 20155.814
## 2486 2180.2326 20155.814
## 2487 2180.2326 20155.814
## 2488 2180.2326 20155.814
## 2489 2180.2326 20155.814
## 2490 2180.2326 20155.814
## 2491 2180.2326 20155.814
## 2492 2180.2326 20155.814
## 2493 2180.2326 20155.814
## 2494 2180.2326 20155.814
## 2495 2180.2326 20155.814
## 2496 2180.2326 20155.814
## 2497 217.1512 1794.767
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## 2501 217.1512 1794.767
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## 2509 217.1512 1794.767
## 2510 217.1512 1794.767
## 2511 217.1512 1794.767
## 2512 217.1512 1794.767
## 2513 217.1512 1794.767
## 2514 217.1512 1794.767
## 2515 217.1512 1794.767
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## 2517 217.1512 1794.767
## 2518 217.1512 1794.767
## 2519 217.1512 1794.767
## 2520 217.1512 1794.767
## 2521 1744.1860 9744.767
## 2522 1744.1860 9744.767
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## 2524 1744.1860 9744.767
## 2525 1744.1860 9744.767
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## 2528 1744.1860 9744.767
## 2529 1744.1860 9744.767
## 2530 1744.1860 9744.767
## 2531 1744.1860 9744.767
## 2532 1744.1860 9744.767
## 2533 1744.1860 9744.767
## 2534 1744.1860 9744.767
## 2535 1744.1860 9744.767
## 2536 1744.1860 9744.767
## 2537 1744.1860 9744.767
## 2538 1744.1860 9744.767
## 2539 1744.1860 9744.767
## 2540 1744.1860 9744.767
## 2541 1744.1860 9744.767
## 2542 1744.1860 9744.767
## 2543 1744.1860 9744.767
## 2544 1744.1860 9744.767
## 2545 1412.7907 17223.837
## 2546 1412.7907 17223.837
## 2547 1412.7907 17223.837
## 2548 1412.7907 17223.837
## 2549 1412.7907 17223.837
## 2550 1412.7907 17223.837
## 2551 1412.7907 17223.837
## 2552 1412.7907 17223.837
## 2553 1412.7907 17223.837
## 2554 1412.7907 17223.837
## 2555 1412.7907 17223.837
## 2556 1412.7907 17223.837
## 2557 1412.7907 17223.837
## 2558 1412.7907 17223.837
## 2559 1412.7907 17223.837
## 2560 1412.7907 17223.837
## 2561 1412.7907 17223.837
## 2562 1412.7907 17223.837
## 2563 1412.7907 17223.837
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## 2565 1412.7907 17223.837
## 2566 1412.7907 17223.837
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## 2568 1412.7907 17223.837
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## 2572 2612.7907 12169.186
## 2573 2612.7907 12169.186
## 2574 2612.7907 12169.186
## 2575 2612.7907 12169.186
## 2576 2612.7907 12169.186
## 2577 2612.7907 12169.186
## 2578 2612.7907 12169.186
## 2579 2612.7907 12169.186
## 2580 2612.7907 12169.186
## 2581 2612.7907 12169.186
## 2582 2612.7907 12169.186
## 2583 2612.7907 12169.186
## 2584 2612.7907 12169.186
## 2585 2612.7907 12169.186
## 2586 2612.7907 12169.186
## 2587 2612.7907 12169.186
## 2588 2612.7907 12169.186
## 2589 2612.7907 12169.186
## 2590 2612.7907 12169.186
## 2591 2612.7907 12169.186
## 2592 2612.7907 12169.186
## 2593 3680.2326 11284.884
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## 2595 3680.2326 11284.884
## 2596 3680.2326 11284.884
## 2597 3680.2326 11284.884
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## 2599 3680.2326 11284.884
## 2600 3680.2326 11284.884
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## 2611 3680.2326 11284.884
## 2612 3680.2326 11284.884
## 2613 3680.2326 11284.884
## 2614 3680.2326 11284.884
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## 3204 2659.8837 7986.628
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## 3208 2659.8837 7986.628
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## 3211 2659.8837 7986.628
## 3212 2659.8837 7986.628
## 3213 2659.8837 7986.628
## 3214 2659.8837 7986.628
## 3215 2659.8837 7986.628
## 3216 2659.8837 7986.628
## 3217 4765.9884 12342.733
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## 3219 4765.9884 12342.733
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## 3221 4765.9884 12342.733
## 3222 4765.9884 12342.733
## 3223 4765.9884 12342.733
## 3224 4765.9884 12342.733
## 3225 4765.9884 12342.733
## total_metaecosystem_Col_indiv total_metaecosystem_Eug_indiv
## 1 4812.20930 7834.88372
## 2 4812.20930 7834.88372
## 3 4812.20930 7834.88372
## 4 4812.20930 7834.88372
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## 10 4812.20930 7834.88372
## 11 4812.20930 7834.88372
## 12 4812.20930 7834.88372
## 13 4812.20930 7834.88372
## 14 4812.20930 7834.88372
## 15 4812.20930 7834.88372
## 16 4812.20930 7834.88372
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## 18 4812.20930 7834.88372
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## 20 4812.20930 7834.88372
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## 22 4812.20930 7834.88372
## 23 4812.20930 7834.88372
## 24 4812.20930 7834.88372
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## 28 20305.81395 3057.55814
## 29 20305.81395 3057.55814
## 30 20305.81395 3057.55814
## 31 20305.81395 3057.55814
## 32 20305.81395 3057.55814
## 33 20305.81395 3057.55814
## 34 20305.81395 3057.55814
## 35 20305.81395 3057.55814
## 36 20305.81395 3057.55814
## 37 20305.81395 3057.55814
## 38 20305.81395 3057.55814
## 39 20305.81395 3057.55814
## 40 20305.81395 3057.55814
## 41 20305.81395 3057.55814
## 42 20305.81395 3057.55814
## 43 20305.81395 3057.55814
## 44 20305.81395 3057.55814
## 45 20305.81395 3057.55814
## 46 20305.81395 3057.55814
## 47 20305.81395 3057.55814
## 48 20305.81395 3057.55814
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## 50 16356.97674 218.02326
## 51 16356.97674 218.02326
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## 59 16356.97674 218.02326
## 60 16356.97674 218.02326
## 61 16356.97674 218.02326
## 62 16356.97674 218.02326
## 63 16356.97674 218.02326
## 64 16356.97674 218.02326
## 65 16356.97674 218.02326
## 66 16356.97674 218.02326
## 67 16356.97674 218.02326
## 68 16356.97674 218.02326
## 69 16356.97674 218.02326
## 70 16356.97674 218.02326
## 71 16356.97674 218.02326
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## 95 6973.25581 0.00000
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## 201 4812.20930 7834.88372
## 202 4812.20930 7834.88372
## 203 4812.20930 7834.88372
## 204 4812.20930 7834.88372
## 205 4812.20930 7834.88372
## 206 4812.20930 7834.88372
## 207 4812.20930 7834.88372
## 208 4812.20930 7834.88372
## 209 4812.20930 7834.88372
## 210 4812.20930 7834.88372
## 211 4812.20930 7834.88372
## 212 4812.20930 7834.88372
## 213 4812.20930 7834.88372
## 214 4812.20930 7834.88372
## 215 4812.20930 7834.88372
## 216 4812.20930 7834.88372
## 217 12404.65116 1941.27907
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## 224 12404.65116 1941.27907
## 225 12404.65116 1941.27907
## 226 12404.65116 1941.27907
## 227 12404.65116 1941.27907
## 228 12404.65116 1941.27907
## 229 12404.65116 1941.27907
## 230 12404.65116 1941.27907
## 231 12404.65116 1941.27907
## 232 12404.65116 1941.27907
## 233 12404.65116 1941.27907
## 234 12404.65116 1941.27907
## 235 12404.65116 1941.27907
## 236 12404.65116 1941.27907
## 237 12404.65116 1941.27907
## 238 12404.65116 1941.27907
## 239 12404.65116 1941.27907
## 240 12404.65116 1941.27907
## 241 5159.30233 218.02326
## 242 5159.30233 218.02326
## 243 5159.30233 218.02326
## 244 5159.30233 218.02326
## 245 5159.30233 218.02326
## 246 5159.30233 218.02326
## 247 5159.30233 218.02326
## 248 5159.30233 218.02326
## 249 5159.30233 218.02326
## 250 5159.30233 218.02326
## 251 5159.30233 218.02326
## 252 5159.30233 218.02326
## 253 5159.30233 218.02326
## 254 5159.30233 218.02326
## 255 5159.30233 218.02326
## 256 5159.30233 218.02326
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## 259 5159.30233 218.02326
## 260 5159.30233 218.02326
## 261 5159.30233 218.02326
## 262 5159.30233 218.02326
## 263 5159.30233 218.02326
## 264 5159.30233 218.02326
## 265 3685.46512 1438.95349
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## 268 3685.46512 1438.95349
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## 271 3685.46512 1438.95349
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## 275 3685.46512 1438.95349
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## 283 3685.46512 1438.95349
## 284 3685.46512 1438.95349
## 285 3685.46512 1438.95349
## 286 3685.46512 1438.95349
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## 396 4812.20930 7834.88372
## 397 4812.20930 7834.88372
## 398 4812.20930 7834.88372
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## 3060 0.00000 1090.11628
## 3061 0.00000 1090.11628
## 3062 0.00000 1090.11628
## 3063 0.00000 1090.11628
## 3064 0.00000 1090.11628
## 3065 0.00000 1090.11628
## 3066 0.00000 1090.11628
## 3067 0.00000 1090.11628
## 3068 0.00000 1090.11628
## 3069 0.00000 1090.11628
## 3070 0.00000 1090.11628
## 3071 0.00000 1090.11628
## 3072 0.00000 1090.11628
## 3073 4812.20930 7834.88372
## 3074 4812.20930 7834.88372
## 3075 4812.20930 7834.88372
## 3076 4812.20930 7834.88372
## 3077 4812.20930 7834.88372
## 3078 4812.20930 7834.88372
## 3079 4812.20930 7834.88372
## 3080 4812.20930 7834.88372
## 3081 4812.20930 7834.88372
## 3082 4812.20930 7834.88372
## 3083 4812.20930 7834.88372
## 3084 4812.20930 7834.88372
## 3085 4812.20930 7834.88372
## 3086 4812.20930 7834.88372
## 3087 4812.20930 7834.88372
## 3088 4812.20930 7834.88372
## 3089 4812.20930 7834.88372
## 3090 4812.20930 7834.88372
## 3091 4812.20930 7834.88372
## 3092 4812.20930 7834.88372
## 3093 4812.20930 7834.88372
## 3094 4812.20930 7834.88372
## 3095 4812.20930 7834.88372
## 3096 4812.20930 7834.88372
## 3097 13489.53488 1281.97674
## 3098 13489.53488 1281.97674
## 3099 13489.53488 1281.97674
## 3100 13489.53488 1281.97674
## 3101 13489.53488 1281.97674
## 3102 13489.53488 1281.97674
## 3103 13489.53488 1281.97674
## 3104 13489.53488 1281.97674
## 3105 13489.53488 1281.97674
## 3106 13489.53488 1281.97674
## 3107 13489.53488 1281.97674
## 3108 13489.53488 1281.97674
## 3109 13489.53488 1281.97674
## 3110 13489.53488 1281.97674
## 3111 13489.53488 1281.97674
## 3112 13489.53488 1281.97674
## 3113 13489.53488 1281.97674
## 3114 13489.53488 1281.97674
## 3115 13489.53488 1281.97674
## 3116 13489.53488 1281.97674
## 3117 13489.53488 1281.97674
## 3118 13489.53488 1281.97674
## 3119 13489.53488 1281.97674
## 3120 13489.53488 1281.97674
## 3121 5752.32558 127.32558
## 3122 5752.32558 127.32558
## 3123 5752.32558 127.32558
## 3124 5752.32558 127.32558
## 3125 5752.32558 127.32558
## 3126 5752.32558 127.32558
## 3127 5752.32558 127.32558
## 3128 5752.32558 127.32558
## 3129 5752.32558 127.32558
## 3130 5752.32558 127.32558
## 3131 5752.32558 127.32558
## 3132 5752.32558 127.32558
## 3133 5752.32558 127.32558
## 3134 5752.32558 127.32558
## 3135 5752.32558 127.32558
## 3136 5752.32558 127.32558
## 3137 5752.32558 127.32558
## 3138 5752.32558 127.32558
## 3139 5752.32558 127.32558
## 3140 5752.32558 127.32558
## 3141 5752.32558 127.32558
## 3142 5752.32558 127.32558
## 3143 5752.32558 127.32558
## 3144 5752.32558 127.32558
## 3145 4046.51163 1438.95349
## 3146 4046.51163 1438.95349
## 3147 4046.51163 1438.95349
## 3148 4046.51163 1438.95349
## 3149 4046.51163 1438.95349
## 3150 4046.51163 1438.95349
## 3151 4046.51163 1438.95349
## 3152 4046.51163 1438.95349
## 3153 4046.51163 1438.95349
## 3154 4046.51163 1438.95349
## 3155 4046.51163 1438.95349
## 3156 4046.51163 1438.95349
## 3157 4046.51163 1438.95349
## 3158 4046.51163 1438.95349
## 3159 4046.51163 1438.95349
## 3160 4046.51163 1438.95349
## 3161 4046.51163 1438.95349
## 3162 4046.51163 1438.95349
## 3163 4046.51163 1438.95349
## 3164 4046.51163 1438.95349
## 3165 4046.51163 1438.95349
## 3166 4046.51163 1438.95349
## 3167 4046.51163 1438.95349
## 3168 4046.51163 1438.95349
## 3169 568.60465 0.00000
## 3170 568.60465 0.00000
## 3171 568.60465 0.00000
## 3172 568.60465 0.00000
## 3173 568.60465 0.00000
## 3174 568.60465 0.00000
## 3175 568.60465 0.00000
## 3176 568.60465 0.00000
## 3177 568.60465 0.00000
## 3178 568.60465 0.00000
## 3179 568.60465 0.00000
## 3180 568.60465 0.00000
## 3181 568.60465 0.00000
## 3182 568.60465 0.00000
## 3183 568.60465 0.00000
## 3184 568.60465 0.00000
## 3185 568.60465 0.00000
## 3186 568.60465 0.00000
## 3187 568.60465 0.00000
## 3188 568.60465 0.00000
## 3189 568.60465 0.00000
## 3190 568.60465 0.00000
## 3191 568.60465 0.00000
## 3192 568.60465 0.00000
## 3193 837.20930 0.00000
## 3194 837.20930 0.00000
## 3195 837.20930 0.00000
## 3196 837.20930 0.00000
## 3197 837.20930 0.00000
## 3198 837.20930 0.00000
## 3199 837.20930 0.00000
## 3200 837.20930 0.00000
## 3201 837.20930 0.00000
## 3202 837.20930 0.00000
## 3203 837.20930 0.00000
## 3204 837.20930 0.00000
## 3205 837.20930 0.00000
## 3206 837.20930 0.00000
## 3207 837.20930 0.00000
## 3208 837.20930 0.00000
## 3209 837.20930 0.00000
## 3210 837.20930 0.00000
## 3211 837.20930 0.00000
## 3212 837.20930 0.00000
## 3213 837.20930 0.00000
## 3214 837.20930 0.00000
## 3215 837.20930 0.00000
## 3216 837.20930 0.00000
## 3217 0.00000 1312.50000
## 3218 0.00000 1312.50000
## 3219 0.00000 1312.50000
## 3220 0.00000 1312.50000
## 3221 0.00000 1312.50000
## 3222 0.00000 1312.50000
## 3223 0.00000 1312.50000
## 3224 0.00000 1312.50000
## 3225 0.00000 1312.50000
## total_metaecosystem_Eup_indiv total_metaecosystem_Lox_indiv
## 1 3155.2326 2494.1860
## 2 3155.2326 2494.1860
## 3 3155.2326 2494.1860
## 4 3155.2326 2494.1860
## 5 3155.2326 2494.1860
## 6 3155.2326 2494.1860
## 7 3155.2326 2494.1860
## 8 3155.2326 2494.1860
## 9 3155.2326 2494.1860
## 10 3155.2326 2494.1860
## 11 3155.2326 2494.1860
## 12 3155.2326 2494.1860
## 13 3155.2326 2494.1860
## 14 3155.2326 2494.1860
## 15 3155.2326 2494.1860
## 16 3155.2326 2494.1860
## 17 3155.2326 2494.1860
## 18 3155.2326 2494.1860
## 19 3155.2326 2494.1860
## 20 3155.2326 2494.1860
## 21 3155.2326 2494.1860
## 22 3155.2326 2494.1860
## 23 3155.2326 2494.1860
## 24 3155.2326 2494.1860
## 25 4484.3023 218.0233
## 26 4484.3023 218.0233
## 27 4484.3023 218.0233
## 28 4484.3023 218.0233
## 29 4484.3023 218.0233
## 30 4484.3023 218.0233
## 31 4484.3023 218.0233
## 32 4484.3023 218.0233
## 33 4484.3023 218.0233
## 34 4484.3023 218.0233
## 35 4484.3023 218.0233
## 36 4484.3023 218.0233
## 37 4484.3023 218.0233
## 38 4484.3023 218.0233
## 39 4484.3023 218.0233
## 40 4484.3023 218.0233
## 41 4484.3023 218.0233
## 42 4484.3023 218.0233
## 43 4484.3023 218.0233
## 44 4484.3023 218.0233
## 45 4484.3023 218.0233
## 46 4484.3023 218.0233
## 47 4484.3023 218.0233
## 48 4484.3023 218.0233
## 49 1318.6047 0.0000
## 50 1318.6047 0.0000
## 51 1318.6047 0.0000
## 52 1318.6047 0.0000
## 53 1318.6047 0.0000
## 54 1318.6047 0.0000
## 55 1318.6047 0.0000
## 56 1318.6047 0.0000
## 57 1318.6047 0.0000
## 58 1318.6047 0.0000
## 59 1318.6047 0.0000
## 60 1318.6047 0.0000
## 61 1318.6047 0.0000
## 62 1318.6047 0.0000
## 63 1318.6047 0.0000
## 64 1318.6047 0.0000
## 65 1318.6047 0.0000
## 66 1318.6047 0.0000
## 67 1318.6047 0.0000
## 68 1318.6047 0.0000
## 69 1318.6047 0.0000
## 70 1318.6047 0.0000
## 71 1318.6047 0.0000
## 72 1318.6047 0.0000
## 73 5084.3023 0.0000
## 74 5084.3023 0.0000
## 75 5084.3023 0.0000
## 76 5084.3023 0.0000
## 77 5084.3023 0.0000
## 78 5084.3023 0.0000
## 79 5084.3023 0.0000
## 80 5084.3023 0.0000
## 81 5084.3023 0.0000
## 82 5084.3023 0.0000
## 83 5084.3023 0.0000
## 84 5084.3023 0.0000
## 85 5084.3023 0.0000
## 86 5084.3023 0.0000
## 87 5084.3023 0.0000
## 88 5084.3023 0.0000
## 89 5084.3023 0.0000
## 90 5084.3023 0.0000
## 91 5084.3023 0.0000
## 92 5084.3023 0.0000
## 93 5084.3023 0.0000
## 94 5084.3023 0.0000
## 95 5084.3023 0.0000
## 96 5084.3023 0.0000
## 97 5241.2791 436.0465
## 98 5241.2791 436.0465
## 99 5241.2791 436.0465
## 100 5241.2791 436.0465
## 101 5241.2791 436.0465
## 102 5241.2791 436.0465
## 103 5241.2791 436.0465
## 104 5241.2791 436.0465
## 105 5241.2791 436.0465
## 106 5241.2791 436.0465
## 107 5241.2791 436.0465
## 108 5241.2791 436.0465
## 109 5241.2791 436.0465
## 110 5241.2791 436.0465
## 111 5241.2791 436.0465
## 112 5241.2791 436.0465
## 113 5241.2791 436.0465
## 114 5241.2791 436.0465
## 115 5241.2791 436.0465
## 116 5241.2791 436.0465
## 117 5241.2791 436.0465
## 118 5241.2791 436.0465
## 119 5241.2791 436.0465
## 120 5241.2791 436.0465
## 121 2956.3953 0.0000
## 122 2956.3953 0.0000
## 123 2956.3953 0.0000
## 124 2956.3953 0.0000
## 125 2956.3953 0.0000
## 126 2956.3953 0.0000
## 127 2956.3953 0.0000
## 128 2956.3953 0.0000
## 129 2956.3953 0.0000
## 130 2956.3953 0.0000
## 131 2956.3953 0.0000
## 132 2956.3953 0.0000
## 133 2956.3953 0.0000
## 134 2956.3953 0.0000
## 135 2956.3953 0.0000
## 136 2956.3953 0.0000
## 137 2956.3953 0.0000
## 138 2956.3953 0.0000
## 139 2956.3953 0.0000
## 140 2956.3953 0.0000
## 141 2956.3953 0.0000
## 142 2956.3953 0.0000
## 143 2956.3953 0.0000
## 144 2956.3953 0.0000
## 145 662.7907 545.0581
## 146 662.7907 545.0581
## 147 662.7907 545.0581
## 148 662.7907 545.0581
## 149 662.7907 545.0581
## 150 662.7907 545.0581
## 151 662.7907 545.0581
## 152 662.7907 545.0581
## 153 662.7907 545.0581
## 154 662.7907 545.0581
## 155 662.7907 545.0581
## 156 662.7907 545.0581
## 157 662.7907 545.0581
## 158 662.7907 545.0581
## 159 662.7907 545.0581
## 160 662.7907 545.0581
## 161 662.7907 545.0581
## 162 662.7907 545.0581
## 163 662.7907 545.0581
## 164 662.7907 545.0581
## 165 662.7907 545.0581
## 166 662.7907 545.0581
## 167 662.7907 545.0581
## 168 662.7907 545.0581
## 169 2428.7791 1630.8140
## 170 2428.7791 1630.8140
## 171 2428.7791 1630.8140
## 172 2428.7791 1630.8140
## 173 2428.7791 1630.8140
## 174 2428.7791 1630.8140
## 175 2428.7791 1630.8140
## 176 2428.7791 1630.8140
## 177 2428.7791 1630.8140
## 178 2428.7791 1630.8140
## 179 2428.7791 1630.8140
## 180 2428.7791 1630.8140
## 181 2428.7791 1630.8140
## 182 2428.7791 1630.8140
## 183 2428.7791 1630.8140
## 184 2428.7791 1630.8140
## 185 2428.7791 1630.8140
## 186 2428.7791 1630.8140
## 187 2428.7791 1630.8140
## 188 2428.7791 1630.8140
## 189 2428.7791 1630.8140
## 190 2428.7791 1630.8140
## 191 2428.7791 1630.8140
## 192 2428.7791 1630.8140
## 193 3155.2326 2494.1860
## 194 3155.2326 2494.1860
## 195 3155.2326 2494.1860
## 196 3155.2326 2494.1860
## 197 3155.2326 2494.1860
## 198 3155.2326 2494.1860
## 199 3155.2326 2494.1860
## 200 3155.2326 2494.1860
## 201 3155.2326 2494.1860
## 202 3155.2326 2494.1860
## 203 3155.2326 2494.1860
## 204 3155.2326 2494.1860
## 205 3155.2326 2494.1860
## 206 3155.2326 2494.1860
## 207 3155.2326 2494.1860
## 208 3155.2326 2494.1860
## 209 3155.2326 2494.1860
## 210 3155.2326 2494.1860
## 211 3155.2326 2494.1860
## 212 3155.2326 2494.1860
## 213 3155.2326 2494.1860
## 214 3155.2326 2494.1860
## 215 3155.2326 2494.1860
## 216 3155.2326 2494.1860
## 217 8312.7907 1438.9535
## 218 8312.7907 1438.9535
## 219 8312.7907 1438.9535
## 220 8312.7907 1438.9535
## 221 8312.7907 1438.9535
## 222 8312.7907 1438.9535
## 223 8312.7907 1438.9535
## 224 8312.7907 1438.9535
## 225 8312.7907 1438.9535
## 226 8312.7907 1438.9535
## 227 8312.7907 1438.9535
## 228 8312.7907 1438.9535
## 229 8312.7907 1438.9535
## 230 8312.7907 1438.9535
## 231 8312.7907 1438.9535
## 232 8312.7907 1438.9535
## 233 8312.7907 1438.9535
## 234 8312.7907 1438.9535
## 235 8312.7907 1438.9535
## 236 8312.7907 1438.9535
## 237 8312.7907 1438.9535
## 238 8312.7907 1438.9535
## 239 8312.7907 1438.9535
## 240 8312.7907 1438.9535
## 241 3071.5116 0.0000
## 242 3071.5116 0.0000
## 243 3071.5116 0.0000
## 244 3071.5116 0.0000
## 245 3071.5116 0.0000
## 246 3071.5116 0.0000
## 247 3071.5116 0.0000
## 248 3071.5116 0.0000
## 249 3071.5116 0.0000
## 250 3071.5116 0.0000
## 251 3071.5116 0.0000
## 252 3071.5116 0.0000
## 253 3071.5116 0.0000
## 254 3071.5116 0.0000
## 255 3071.5116 0.0000
## 256 3071.5116 0.0000
## 257 3071.5116 0.0000
## 258 3071.5116 0.0000
## 259 3071.5116 0.0000
## 260 3071.5116 0.0000
## 261 3071.5116 0.0000
## 262 3071.5116 0.0000
## 263 3071.5116 0.0000
## 264 3071.5116 0.0000
## 265 4988.3721 0.0000
## 266 4988.3721 0.0000
## 267 4988.3721 0.0000
## 268 4988.3721 0.0000
## 269 4988.3721 0.0000
## 270 4988.3721 0.0000
## 271 4988.3721 0.0000
## 272 4988.3721 0.0000
## 273 4988.3721 0.0000
## 274 4988.3721 0.0000
## 275 4988.3721 0.0000
## 276 4988.3721 0.0000
## 277 4988.3721 0.0000
## 278 4988.3721 0.0000
## 279 4988.3721 0.0000
## 280 4988.3721 0.0000
## 281 4988.3721 0.0000
## 282 4988.3721 0.0000
## 283 4988.3721 0.0000
## 284 4988.3721 0.0000
## 285 4988.3721 0.0000
## 286 4988.3721 0.0000
## 287 4988.3721 0.0000
## 288 4988.3721 0.0000
## 289 4534.8837 436.0465
## 290 4534.8837 436.0465
## 291 4534.8837 436.0465
## 292 4534.8837 436.0465
## 293 4534.8837 436.0465
## 294 4534.8837 436.0465
## 295 4534.8837 436.0465
## 296 4534.8837 436.0465
## 297 4534.8837 436.0465
## 298 4534.8837 436.0465
## 299 4534.8837 436.0465
## 300 4534.8837 436.0465
## 301 4534.8837 436.0465
## 302 4534.8837 436.0465
## 303 4534.8837 436.0465
## 304 4534.8837 436.0465
## 305 4534.8837 436.0465
## 306 4534.8837 436.0465
## 307 4534.8837 436.0465
## 308 4534.8837 436.0465
## 309 4534.8837 436.0465
## 310 4534.8837 436.0465
## 311 4534.8837 436.0465
## 312 4534.8837 436.0465
## 313 1456.3953 0.0000
## 314 1456.3953 0.0000
## 315 1456.3953 0.0000
## 316 1456.3953 0.0000
## 317 1456.3953 0.0000
## 318 1456.3953 0.0000
## 319 1456.3953 0.0000
## 320 1456.3953 0.0000
## 321 1456.3953 0.0000
## 322 1456.3953 0.0000
## 323 1456.3953 0.0000
## 324 1456.3953 0.0000
## 325 1456.3953 0.0000
## 326 1456.3953 0.0000
## 327 1456.3953 0.0000
## 328 1456.3953 0.0000
## 329 1456.3953 0.0000
## 330 1456.3953 0.0000
## 331 1456.3953 0.0000
## 332 1456.3953 0.0000
## 333 1456.3953 0.0000
## 334 1456.3953 0.0000
## 335 1456.3953 0.0000
## 336 1456.3953 0.0000
## 337 1059.5930 0.0000
## 338 1059.5930 0.0000
## 339 1059.5930 0.0000
## 340 1059.5930 0.0000
## 341 1059.5930 0.0000
## 342 1059.5930 0.0000
## 343 1059.5930 0.0000
## 344 1059.5930 0.0000
## 345 1059.5930 0.0000
## 346 1059.5930 0.0000
## 347 1059.5930 0.0000
## 348 1059.5930 0.0000
## 349 1059.5930 0.0000
## 350 1059.5930 0.0000
## 351 1059.5930 0.0000
## 352 1059.5930 0.0000
## 353 1059.5930 0.0000
## 354 1059.5930 0.0000
## 355 1059.5930 0.0000
## 356 1059.5930 0.0000
## 357 1059.5930 0.0000
## 358 1059.5930 0.0000
## 359 1059.5930 0.0000
## 360 1059.5930 0.0000
## 361 1360.4651 545.0581
## 362 1360.4651 545.0581
## 363 1360.4651 545.0581
## 364 1360.4651 545.0581
## 365 1360.4651 545.0581
## 366 1360.4651 545.0581
## 367 1360.4651 545.0581
## 368 1360.4651 545.0581
## 369 1360.4651 545.0581
## 370 1360.4651 545.0581
## 371 1360.4651 545.0581
## 372 1360.4651 545.0581
## 373 1360.4651 545.0581
## 374 1360.4651 545.0581
## 375 1360.4651 545.0581
## 376 1360.4651 545.0581
## 377 1360.4651 545.0581
## 378 1360.4651 545.0581
## 379 1360.4651 545.0581
## 380 1360.4651 545.0581
## 381 1360.4651 545.0581
## 382 1360.4651 545.0581
## 383 1360.4651 545.0581
## 384 1360.4651 545.0581
## 385 3155.2326 2494.1860
## 386 3155.2326 2494.1860
## 387 3155.2326 2494.1860
## 388 3155.2326 2494.1860
## 389 3155.2326 2494.1860
## 390 3155.2326 2494.1860
## 391 3155.2326 2494.1860
## 392 3155.2326 2494.1860
## 393 3155.2326 2494.1860
## 394 3155.2326 2494.1860
## 395 3155.2326 2494.1860
## 396 3155.2326 2494.1860
## 397 3155.2326 2494.1860
## 398 3155.2326 2494.1860
## 399 3155.2326 2494.1860
## 400 3155.2326 2494.1860
## 401 3155.2326 2494.1860
## 402 3155.2326 2494.1860
## 403 3155.2326 2494.1860
## 404 3155.2326 2494.1860
## 405 3155.2326 2494.1860
## 406 3155.2326 2494.1860
## 407 3155.2326 2494.1860
## 408 3155.2326 2494.1860
## 409 2190.6977 2188.9535
## 410 2190.6977 2188.9535
## 411 2190.6977 2188.9535
## 412 2190.6977 2188.9535
## 413 2190.6977 2188.9535
## 414 2190.6977 2188.9535
## 415 2190.6977 2188.9535
## 416 2190.6977 2188.9535
## 417 2190.6977 2188.9535
## 418 2190.6977 2188.9535
## 419 2190.6977 2188.9535
## 420 2190.6977 2188.9535
## 421 2190.6977 2188.9535
## 422 2190.6977 2188.9535
## 423 2190.6977 2188.9535
## 424 2190.6977 2188.9535
## 425 2190.6977 2188.9535
## 426 2190.6977 2188.9535
## 427 2190.6977 2188.9535
## 428 2190.6977 2188.9535
## 429 2190.6977 2188.9535
## 430 2190.6977 2188.9535
## 431 2190.6977 2188.9535
## 432 2190.6977 2188.9535
## 433 6586.0465 244.1860
## 434 6586.0465 244.1860
## 435 6586.0465 244.1860
## 436 6586.0465 244.1860
## 437 6586.0465 244.1860
## 438 6586.0465 244.1860
## 439 6586.0465 244.1860
## 440 6586.0465 244.1860
## 441 6586.0465 244.1860
## 442 6586.0465 244.1860
## 443 6586.0465 244.1860
## 444 6586.0465 244.1860
## 445 6586.0465 244.1860
## 446 6586.0465 244.1860
## 447 6586.0465 244.1860
## 448 6586.0465 244.1860
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## 2848 1046.5116 1521.8023
## 2849 1046.5116 1521.8023
## 2850 1046.5116 1521.8023
## 2851 1046.5116 1521.8023
## 2852 1046.5116 1521.8023
## 2853 1046.5116 1521.8023
## 2854 1046.5116 1521.8023
## 2855 1046.5116 1521.8023
## 2856 1046.5116 1521.8023
## 2857 1090.1163 545.0581
## 2858 1090.1163 545.0581
## 2859 1090.1163 545.0581
## 2860 1090.1163 545.0581
## 2861 1090.1163 545.0581
## 2862 1090.1163 545.0581
## 2863 1090.1163 545.0581
## 2864 1090.1163 545.0581
## 2865 1090.1163 545.0581
## 2866 1090.1163 545.0581
## 2867 1090.1163 545.0581
## 2868 1090.1163 545.0581
## 2869 1090.1163 545.0581
## 2870 1090.1163 545.0581
## 2871 1090.1163 545.0581
## 2872 1090.1163 545.0581
## 2873 1090.1163 545.0581
## 2874 1090.1163 545.0581
## 2875 1090.1163 545.0581
## 2876 1090.1163 545.0581
## 2877 1090.1163 545.0581
## 2878 1090.1163 545.0581
## 2879 1090.1163 545.0581
## 2880 1090.1163 545.0581
## 2881 3155.2326 2494.1860
## 2882 3155.2326 2494.1860
## 2883 3155.2326 2494.1860
## 2884 3155.2326 2494.1860
## 2885 3155.2326 2494.1860
## 2886 3155.2326 2494.1860
## 2887 3155.2326 2494.1860
## 2888 3155.2326 2494.1860
## 2889 3155.2326 2494.1860
## 2890 3155.2326 2494.1860
## 2891 3155.2326 2494.1860
## 2892 3155.2326 2494.1860
## 2893 3155.2326 2494.1860
## 2894 3155.2326 2494.1860
## 2895 3155.2326 2494.1860
## 2896 3155.2326 2494.1860
## 2897 3155.2326 2494.1860
## 2898 3155.2326 2494.1860
## 2899 3155.2326 2494.1860
## 2900 3155.2326 2494.1860
## 2901 3155.2326 2494.1860
## 2902 3155.2326 2494.1860
## 2903 3155.2326 2494.1860
## 2904 3155.2326 2494.1860
## 2905 3811.0465 0.0000
## 2906 3811.0465 0.0000
## 2907 3811.0465 0.0000
## 2908 3811.0465 0.0000
## 2909 3811.0465 0.0000
## 2910 3811.0465 0.0000
## 2911 3811.0465 0.0000
## 2912 3811.0465 0.0000
## 2913 3811.0465 0.0000
## 2914 3811.0465 0.0000
## 2915 3811.0465 0.0000
## 2916 3811.0465 0.0000
## 2917 3811.0465 0.0000
## 2918 3811.0465 0.0000
## 2919 3811.0465 0.0000
## 2920 3811.0465 0.0000
## 2921 3811.0465 0.0000
## 2922 3811.0465 0.0000
## 2923 3811.0465 0.0000
## 2924 3811.0465 0.0000
## 2925 3811.0465 0.0000
## 2926 3811.0465 0.0000
## 2927 3811.0465 0.0000
## 2928 3811.0465 0.0000
## 2929 1887.2093 218.0233
## 2930 1887.2093 218.0233
## 2931 1887.2093 218.0233
## 2932 1887.2093 218.0233
## 2933 1887.2093 218.0233
## 2934 1887.2093 218.0233
## 2935 1887.2093 218.0233
## 2936 1887.2093 218.0233
## 2937 1887.2093 218.0233
## 2938 1887.2093 218.0233
## 2939 1887.2093 218.0233
## 2940 1887.2093 218.0233
## 2941 1887.2093 218.0233
## 2942 1887.2093 218.0233
## 2943 1887.2093 218.0233
## 2944 1887.2093 218.0233
## 2945 1887.2093 218.0233
## 2946 1887.2093 218.0233
## 2947 1887.2093 218.0233
## 2948 1887.2093 218.0233
## 2949 1887.2093 218.0233
## 2950 1887.2093 218.0233
## 2951 1887.2093 218.0233
## 2952 1887.2093 218.0233
## 2953 5084.3023 0.0000
## 2954 5084.3023 0.0000
## 2955 5084.3023 0.0000
## 2956 5084.3023 0.0000
## 2957 5084.3023 0.0000
## 2958 5084.3023 0.0000
## 2959 5084.3023 0.0000
## 2960 5084.3023 0.0000
## 2961 5084.3023 0.0000
## 2962 5084.3023 0.0000
## 2963 5084.3023 0.0000
## 2964 5084.3023 0.0000
## 2965 5084.3023 0.0000
## 2966 5084.3023 0.0000
## 2967 5084.3023 0.0000
## 2968 5084.3023 0.0000
## 2969 5084.3023 0.0000
## 2970 5084.3023 0.0000
## 2971 5084.3023 0.0000
## 2972 5084.3023 0.0000
## 2973 5084.3023 0.0000
## 2974 5084.3023 0.0000
## 2975 5084.3023 0.0000
## 2976 5084.3023 0.0000
## 2977 4822.6744 0.0000
## 2978 4822.6744 0.0000
## 2979 4822.6744 0.0000
## 2980 4822.6744 0.0000
## 2981 4822.6744 0.0000
## 2982 4822.6744 0.0000
## 2983 4822.6744 0.0000
## 2984 4822.6744 0.0000
## 2985 4822.6744 0.0000
## 2986 4822.6744 0.0000
## 2987 4822.6744 0.0000
## 2988 4822.6744 0.0000
## 2989 4822.6744 0.0000
## 2990 4822.6744 0.0000
## 2991 4822.6744 0.0000
## 2992 4822.6744 0.0000
## 2993 4822.6744 0.0000
## 2994 4822.6744 0.0000
## 2995 4822.6744 0.0000
## 2996 4822.6744 0.0000
## 2997 4822.6744 0.0000
## 2998 4822.6744 0.0000
## 2999 4822.6744 0.0000
## 3000 4822.6744 0.0000
## 3001 3174.4186 0.0000
## 3002 3174.4186 0.0000
## 3003 3174.4186 0.0000
## 3004 3174.4186 0.0000
## 3005 3174.4186 0.0000
## 3006 3174.4186 0.0000
## 3007 3174.4186 0.0000
## 3008 3174.4186 0.0000
## 3009 3174.4186 0.0000
## 3010 3174.4186 0.0000
## 3011 3174.4186 0.0000
## 3012 3174.4186 0.0000
## 3013 3174.4186 0.0000
## 3014 3174.4186 0.0000
## 3015 3174.4186 0.0000
## 3016 3174.4186 0.0000
## 3017 3174.4186 0.0000
## 3018 3174.4186 0.0000
## 3019 3174.4186 0.0000
## 3020 3174.4186 0.0000
## 3021 3174.4186 0.0000
## 3022 3174.4186 0.0000
## 3023 3174.4186 0.0000
## 3024 3174.4186 0.0000
## 3025 662.7907 545.0581
## 3026 662.7907 545.0581
## 3027 662.7907 545.0581
## 3028 662.7907 545.0581
## 3029 662.7907 545.0581
## 3030 662.7907 545.0581
## 3031 662.7907 545.0581
## 3032 662.7907 545.0581
## 3033 662.7907 545.0581
## 3034 662.7907 545.0581
## 3035 662.7907 545.0581
## 3036 662.7907 545.0581
## 3037 662.7907 545.0581
## 3038 662.7907 545.0581
## 3039 662.7907 545.0581
## 3040 662.7907 545.0581
## 3041 662.7907 545.0581
## 3042 662.7907 545.0581
## 3043 662.7907 545.0581
## 3044 662.7907 545.0581
## 3045 662.7907 545.0581
## 3046 662.7907 545.0581
## 3047 662.7907 545.0581
## 3048 662.7907 545.0581
## 3049 2646.8023 1630.8140
## 3050 2646.8023 1630.8140
## 3051 2646.8023 1630.8140
## 3052 2646.8023 1630.8140
## 3053 2646.8023 1630.8140
## 3054 2646.8023 1630.8140
## 3055 2646.8023 1630.8140
## 3056 2646.8023 1630.8140
## 3057 2646.8023 1630.8140
## 3058 2646.8023 1630.8140
## 3059 2646.8023 1630.8140
## 3060 2646.8023 1630.8140
## 3061 2646.8023 1630.8140
## 3062 2646.8023 1630.8140
## 3063 2646.8023 1630.8140
## 3064 2646.8023 1630.8140
## 3065 2646.8023 1630.8140
## 3066 2646.8023 1630.8140
## 3067 2646.8023 1630.8140
## 3068 2646.8023 1630.8140
## 3069 2646.8023 1630.8140
## 3070 2646.8023 1630.8140
## 3071 2646.8023 1630.8140
## 3072 2646.8023 1630.8140
## 3073 3155.2326 2494.1860
## 3074 3155.2326 2494.1860
## 3075 3155.2326 2494.1860
## 3076 3155.2326 2494.1860
## 3077 3155.2326 2494.1860
## 3078 3155.2326 2494.1860
## 3079 3155.2326 2494.1860
## 3080 3155.2326 2494.1860
## 3081 3155.2326 2494.1860
## 3082 3155.2326 2494.1860
## 3083 3155.2326 2494.1860
## 3084 3155.2326 2494.1860
## 3085 3155.2326 2494.1860
## 3086 3155.2326 2494.1860
## 3087 3155.2326 2494.1860
## 3088 3155.2326 2494.1860
## 3089 3155.2326 2494.1860
## 3090 3155.2326 2494.1860
## 3091 3155.2326 2494.1860
## 3092 3155.2326 2494.1860
## 3093 3155.2326 2494.1860
## 3094 3155.2326 2494.1860
## 3095 3155.2326 2494.1860
## 3096 3155.2326 2494.1860
## 3097 7639.5349 1220.9302
## 3098 7639.5349 1220.9302
## 3099 7639.5349 1220.9302
## 3100 7639.5349 1220.9302
## 3101 7639.5349 1220.9302
## 3102 7639.5349 1220.9302
## 3103 7639.5349 1220.9302
## 3104 7639.5349 1220.9302
## 3105 7639.5349 1220.9302
## 3106 7639.5349 1220.9302
## 3107 7639.5349 1220.9302
## 3108 7639.5349 1220.9302
## 3109 7639.5349 1220.9302
## 3110 7639.5349 1220.9302
## 3111 7639.5349 1220.9302
## 3112 7639.5349 1220.9302
## 3113 7639.5349 1220.9302
## 3114 7639.5349 1220.9302
## 3115 7639.5349 1220.9302
## 3116 7639.5349 1220.9302
## 3117 7639.5349 1220.9302
## 3118 7639.5349 1220.9302
## 3119 7639.5349 1220.9302
## 3120 7639.5349 1220.9302
## 3121 3640.1163 218.0233
## 3122 3640.1163 218.0233
## 3123 3640.1163 218.0233
## 3124 3640.1163 218.0233
## 3125 3640.1163 218.0233
## 3126 3640.1163 218.0233
## 3127 3640.1163 218.0233
## 3128 3640.1163 218.0233
## 3129 3640.1163 218.0233
## 3130 3640.1163 218.0233
## 3131 3640.1163 218.0233
## 3132 3640.1163 218.0233
## 3133 3640.1163 218.0233
## 3134 3640.1163 218.0233
## 3135 3640.1163 218.0233
## 3136 3640.1163 218.0233
## 3137 3640.1163 218.0233
## 3138 3640.1163 218.0233
## 3139 3640.1163 218.0233
## 3140 3640.1163 218.0233
## 3141 3640.1163 218.0233
## 3142 3640.1163 218.0233
## 3143 3640.1163 218.0233
## 3144 3640.1163 218.0233
## 3145 4988.3721 0.0000
## 3146 4988.3721 0.0000
## 3147 4988.3721 0.0000
## 3148 4988.3721 0.0000
## 3149 4988.3721 0.0000
## 3150 4988.3721 0.0000
## 3151 4988.3721 0.0000
## 3152 4988.3721 0.0000
## 3153 4988.3721 0.0000
## 3154 4988.3721 0.0000
## 3155 4988.3721 0.0000
## 3156 4988.3721 0.0000
## 3157 4988.3721 0.0000
## 3158 4988.3721 0.0000
## 3159 4988.3721 0.0000
## 3160 4988.3721 0.0000
## 3161 4988.3721 0.0000
## 3162 4988.3721 0.0000
## 3163 4988.3721 0.0000
## 3164 4988.3721 0.0000
## 3165 4988.3721 0.0000
## 3166 4988.3721 0.0000
## 3167 4988.3721 0.0000
## 3168 4988.3721 0.0000
## 3169 4116.2791 0.0000
## 3170 4116.2791 0.0000
## 3171 4116.2791 0.0000
## 3172 4116.2791 0.0000
## 3173 4116.2791 0.0000
## 3174 4116.2791 0.0000
## 3175 4116.2791 0.0000
## 3176 4116.2791 0.0000
## 3177 4116.2791 0.0000
## 3178 4116.2791 0.0000
## 3179 4116.2791 0.0000
## 3180 4116.2791 0.0000
## 3181 4116.2791 0.0000
## 3182 4116.2791 0.0000
## 3183 4116.2791 0.0000
## 3184 4116.2791 0.0000
## 3185 4116.2791 0.0000
## 3186 4116.2791 0.0000
## 3187 4116.2791 0.0000
## 3188 4116.2791 0.0000
## 3189 4116.2791 0.0000
## 3190 4116.2791 0.0000
## 3191 4116.2791 0.0000
## 3192 4116.2791 0.0000
## 3193 1674.4186 0.0000
## 3194 1674.4186 0.0000
## 3195 1674.4186 0.0000
## 3196 1674.4186 0.0000
## 3197 1674.4186 0.0000
## 3198 1674.4186 0.0000
## 3199 1674.4186 0.0000
## 3200 1674.4186 0.0000
## 3201 1674.4186 0.0000
## 3202 1674.4186 0.0000
## 3203 1674.4186 0.0000
## 3204 1674.4186 0.0000
## 3205 1674.4186 0.0000
## 3206 1674.4186 0.0000
## 3207 1674.4186 0.0000
## 3208 1674.4186 0.0000
## 3209 1674.4186 0.0000
## 3210 1674.4186 0.0000
## 3211 1674.4186 0.0000
## 3212 1674.4186 0.0000
## 3213 1674.4186 0.0000
## 3214 1674.4186 0.0000
## 3215 1674.4186 0.0000
## 3216 1674.4186 0.0000
## 3217 1059.5930 0.0000
## 3218 1059.5930 0.0000
## 3219 1059.5930 0.0000
## 3220 1059.5930 0.0000
## 3221 1059.5930 0.0000
## 3222 1059.5930 0.0000
## 3223 1059.5930 0.0000
## 3224 1059.5930 0.0000
## 3225 1059.5930 0.0000
## total_metaecosystem_Pau_indiv total_metaecosystem_Pca_indiv
## 1 5161.0465 883.43023
## 2 5161.0465 883.43023
## 3 5161.0465 883.43023
## 4 5161.0465 883.43023
## 5 5161.0465 883.43023
## 6 5161.0465 883.43023
## 7 5161.0465 883.43023
## 8 5161.0465 883.43023
## 9 5161.0465 883.43023
## 10 5161.0465 883.43023
## 11 5161.0465 883.43023
## 12 5161.0465 883.43023
## 13 5161.0465 883.43023
## 14 5161.0465 883.43023
## 15 5161.0465 883.43023
## 16 5161.0465 883.43023
## 17 5161.0465 883.43023
## 18 5161.0465 883.43023
## 19 5161.0465 883.43023
## 20 5161.0465 883.43023
## 21 5161.0465 883.43023
## 22 5161.0465 883.43023
## 23 5161.0465 883.43023
## 24 5161.0465 883.43023
## 25 0.0000 1854.06977
## 26 0.0000 1854.06977
## 27 0.0000 1854.06977
## 28 0.0000 1854.06977
## 29 0.0000 1854.06977
## 30 0.0000 1854.06977
## 31 0.0000 1854.06977
## 32 0.0000 1854.06977
## 33 0.0000 1854.06977
## 34 0.0000 1854.06977
## 35 0.0000 1854.06977
## 36 0.0000 1854.06977
## 37 0.0000 1854.06977
## 38 0.0000 1854.06977
## 39 0.0000 1854.06977
## 40 0.0000 1854.06977
## 41 0.0000 1854.06977
## 42 0.0000 1854.06977
## 43 0.0000 1854.06977
## 44 0.0000 1854.06977
## 45 0.0000 1854.06977
## 46 0.0000 1854.06977
## 47 0.0000 1854.06977
## 48 0.0000 1854.06977
## 49 1970.9302 1189.53488
## 50 1970.9302 1189.53488
## 51 1970.9302 1189.53488
## 52 1970.9302 1189.53488
## 53 1970.9302 1189.53488
## 54 1970.9302 1189.53488
## 55 1970.9302 1189.53488
## 56 1970.9302 1189.53488
## 57 1970.9302 1189.53488
## 58 1970.9302 1189.53488
## 59 1970.9302 1189.53488
## 60 1970.9302 1189.53488
## 61 1970.9302 1189.53488
## 62 1970.9302 1189.53488
## 63 1970.9302 1189.53488
## 64 1970.9302 1189.53488
## 65 1970.9302 1189.53488
## 66 1970.9302 1189.53488
## 67 1970.9302 1189.53488
## 68 1970.9302 1189.53488
## 69 1970.9302 1189.53488
## 70 1970.9302 1189.53488
## 71 1970.9302 1189.53488
## 72 1970.9302 1189.53488
## 73 1369.1860 3783.13953
## 74 1369.1860 3783.13953
## 75 1369.1860 3783.13953
## 76 1369.1860 3783.13953
## 77 1369.1860 3783.13953
## 78 1369.1860 3783.13953
## 79 1369.1860 3783.13953
## 80 1369.1860 3783.13953
## 81 1369.1860 3783.13953
## 82 1369.1860 3783.13953
## 83 1369.1860 3783.13953
## 84 1369.1860 3783.13953
## 85 1369.1860 3783.13953
## 86 1369.1860 3783.13953
## 87 1369.1860 3783.13953
## 88 1369.1860 3783.13953
## 89 1369.1860 3783.13953
## 90 1369.1860 3783.13953
## 91 1369.1860 3783.13953
## 92 1369.1860 3783.13953
## 93 1369.1860 3783.13953
## 94 1369.1860 3783.13953
## 95 1369.1860 3783.13953
## 96 1369.1860 3783.13953
## 97 2776.7442 1709.30233
## 98 2776.7442 1709.30233
## 99 2776.7442 1709.30233
## 100 2776.7442 1709.30233
## 101 2776.7442 1709.30233
## 102 2776.7442 1709.30233
## 103 2776.7442 1709.30233
## 104 2776.7442 1709.30233
## 105 2776.7442 1709.30233
## 106 2776.7442 1709.30233
## 107 2776.7442 1709.30233
## 108 2776.7442 1709.30233
## 109 2776.7442 1709.30233
## 110 2776.7442 1709.30233
## 111 2776.7442 1709.30233
## 112 2776.7442 1709.30233
## 113 2776.7442 1709.30233
## 114 2776.7442 1709.30233
## 115 2776.7442 1709.30233
## 116 2776.7442 1709.30233
## 117 2776.7442 1709.30233
## 118 2776.7442 1709.30233
## 119 2776.7442 1709.30233
## 120 2776.7442 1709.30233
## 121 559.8837 540.69767
## 122 559.8837 540.69767
## 123 559.8837 540.69767
## 124 559.8837 540.69767
## 125 559.8837 540.69767
## 126 559.8837 540.69767
## 127 559.8837 540.69767
## 128 559.8837 540.69767
## 129 559.8837 540.69767
## 130 559.8837 540.69767
## 131 559.8837 540.69767
## 132 559.8837 540.69767
## 133 559.8837 540.69767
## 134 559.8837 540.69767
## 135 559.8837 540.69767
## 136 559.8837 540.69767
## 137 559.8837 540.69767
## 138 559.8837 540.69767
## 139 559.8837 540.69767
## 140 559.8837 540.69767
## 141 559.8837 540.69767
## 142 559.8837 540.69767
## 143 559.8837 540.69767
## 144 559.8837 540.69767
## 145 109.0116 1181.68605
## 146 109.0116 1181.68605
## 147 109.0116 1181.68605
## 148 109.0116 1181.68605
## 149 109.0116 1181.68605
## 150 109.0116 1181.68605
## 151 109.0116 1181.68605
## 152 109.0116 1181.68605
## 153 109.0116 1181.68605
## 154 109.0116 1181.68605
## 155 109.0116 1181.68605
## 156 109.0116 1181.68605
## 157 109.0116 1181.68605
## 158 109.0116 1181.68605
## 159 109.0116 1181.68605
## 160 109.0116 1181.68605
## 161 109.0116 1181.68605
## 162 109.0116 1181.68605
## 163 109.0116 1181.68605
## 164 109.0116 1181.68605
## 165 109.0116 1181.68605
## 166 109.0116 1181.68605
## 167 109.0116 1181.68605
## 168 109.0116 1181.68605
## 169 531.9767 1063.95349
## 170 531.9767 1063.95349
## 171 531.9767 1063.95349
## 172 531.9767 1063.95349
## 173 531.9767 1063.95349
## 174 531.9767 1063.95349
## 175 531.9767 1063.95349
## 176 531.9767 1063.95349
## 177 531.9767 1063.95349
## 178 531.9767 1063.95349
## 179 531.9767 1063.95349
## 180 531.9767 1063.95349
## 181 531.9767 1063.95349
## 182 531.9767 1063.95349
## 183 531.9767 1063.95349
## 184 531.9767 1063.95349
## 185 531.9767 1063.95349
## 186 531.9767 1063.95349
## 187 531.9767 1063.95349
## 188 531.9767 1063.95349
## 189 531.9767 1063.95349
## 190 531.9767 1063.95349
## 191 531.9767 1063.95349
## 192 531.9767 1063.95349
## 193 5161.0465 883.43023
## 194 5161.0465 883.43023
## 195 5161.0465 883.43023
## 196 5161.0465 883.43023
## 197 5161.0465 883.43023
## 198 5161.0465 883.43023
## 199 5161.0465 883.43023
## 200 5161.0465 883.43023
## 201 5161.0465 883.43023
## 202 5161.0465 883.43023
## 203 5161.0465 883.43023
## 204 5161.0465 883.43023
## 205 5161.0465 883.43023
## 206 5161.0465 883.43023
## 207 5161.0465 883.43023
## 208 5161.0465 883.43023
## 209 5161.0465 883.43023
## 210 5161.0465 883.43023
## 211 5161.0465 883.43023
## 212 5161.0465 883.43023
## 213 5161.0465 883.43023
## 214 5161.0465 883.43023
## 215 5161.0465 883.43023
## 216 5161.0465 883.43023
## 217 5720.9302 5708.72093
## 218 5720.9302 5708.72093
## 219 5720.9302 5708.72093
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## 1971 1854.0698 1090.11628
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## 1974 1854.0698 1090.11628
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## 1977 1854.0698 1090.11628
## 1978 1854.0698 1090.11628
## 1979 1854.0698 1090.11628
## 1980 1854.0698 1090.11628
## 1981 1854.0698 1090.11628
## 1982 1854.0698 1090.11628
## 1983 1854.0698 1090.11628
## 1984 1854.0698 1090.11628
## 1985 1854.0698 1090.11628
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## 1987 1854.0698 1090.11628
## 1988 1854.0698 1090.11628
## 1989 1854.0698 1090.11628
## 1990 1854.0698 1090.11628
## 1991 1854.0698 1090.11628
## 1992 1854.0698 1090.11628
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## 1994 1852.3256 3636.62791
## 1995 1852.3256 3636.62791
## 1996 1852.3256 3636.62791
## 1997 1852.3256 3636.62791
## 1998 1852.3256 3636.62791
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## 3166 3052.3256 0.00000
## 3167 3052.3256 0.00000
## 3168 3052.3256 0.00000
## 3169 1948.2558 0.00000
## 3170 1948.2558 0.00000
## 3171 1948.2558 0.00000
## 3172 1948.2558 0.00000
## 3173 1948.2558 0.00000
## 3174 1948.2558 0.00000
## 3175 1948.2558 0.00000
## 3176 1948.2558 0.00000
## 3177 1948.2558 0.00000
## 3178 1948.2558 0.00000
## 3179 1948.2558 0.00000
## 3180 1948.2558 0.00000
## 3181 1948.2558 0.00000
## 3182 1948.2558 0.00000
## 3183 1948.2558 0.00000
## 3184 1948.2558 0.00000
## 3185 1948.2558 0.00000
## 3186 1948.2558 0.00000
## 3187 1948.2558 0.00000
## 3188 1948.2558 0.00000
## 3189 1948.2558 0.00000
## 3190 1948.2558 0.00000
## 3191 1948.2558 0.00000
## 3192 1948.2558 0.00000
## 3193 1665.6977 1030.81395
## 3194 1665.6977 1030.81395
## 3195 1665.6977 1030.81395
## 3196 1665.6977 1030.81395
## 3197 1665.6977 1030.81395
## 3198 1665.6977 1030.81395
## 3199 1665.6977 1030.81395
## 3200 1665.6977 1030.81395
## 3201 1665.6977 1030.81395
## 3202 1665.6977 1030.81395
## 3203 1665.6977 1030.81395
## 3204 1665.6977 1030.81395
## 3205 1665.6977 1030.81395
## 3206 1665.6977 1030.81395
## 3207 1665.6977 1030.81395
## 3208 1665.6977 1030.81395
## 3209 1665.6977 1030.81395
## 3210 1665.6977 1030.81395
## 3211 1665.6977 1030.81395
## 3212 1665.6977 1030.81395
## 3213 1665.6977 1030.81395
## 3214 1665.6977 1030.81395
## 3215 1665.6977 1030.81395
## 3216 1665.6977 1030.81395
## 3217 1125.0000 1360.46512
## 3218 1125.0000 1360.46512
## 3219 1125.0000 1360.46512
## 3220 1125.0000 1360.46512
## 3221 1125.0000 1360.46512
## 3222 1125.0000 1360.46512
## 3223 1125.0000 1360.46512
## 3224 1125.0000 1360.46512
## 3225 1125.0000 1360.46512
## total_metaecosystem_Spi_indiv total_metaecosystem_Spi_te_indiv
## 1 635.75581 981.9767
## 2 635.75581 981.9767
## 3 635.75581 981.9767
## 4 635.75581 981.9767
## 5 635.75581 981.9767
## 6 635.75581 981.9767
## 7 635.75581 981.9767
## 8 635.75581 981.9767
## 9 635.75581 981.9767
## 10 635.75581 981.9767
## 11 635.75581 981.9767
## 12 635.75581 981.9767
## 13 635.75581 981.9767
## 14 635.75581 981.9767
## 15 635.75581 981.9767
## 16 635.75581 981.9767
## 17 635.75581 981.9767
## 18 635.75581 981.9767
## 19 635.75581 981.9767
## 20 635.75581 981.9767
## 21 635.75581 981.9767
## 22 635.75581 981.9767
## 23 635.75581 981.9767
## 24 635.75581 981.9767
## 25 1055.23256 1090.1163
## 26 1055.23256 1090.1163
## 27 1055.23256 1090.1163
## 28 1055.23256 1090.1163
## 29 1055.23256 1090.1163
## 30 1055.23256 1090.1163
## 31 1055.23256 1090.1163
## 32 1055.23256 1090.1163
## 33 1055.23256 1090.1163
## 34 1055.23256 1090.1163
## 35 1055.23256 1090.1163
## 36 1055.23256 1090.1163
## 37 1055.23256 1090.1163
## 38 1055.23256 1090.1163
## 39 1055.23256 1090.1163
## 40 1055.23256 1090.1163
## 41 1055.23256 1090.1163
## 42 1055.23256 1090.1163
## 43 1055.23256 1090.1163
## 44 1055.23256 1090.1163
## 45 1055.23256 1090.1163
## 46 1055.23256 1090.1163
## 47 1055.23256 1090.1163
## 48 1055.23256 1090.1163
## 49 1090.11628 2084.3023
## 50 1090.11628 2084.3023
## 51 1090.11628 2084.3023
## 52 1090.11628 2084.3023
## 53 1090.11628 2084.3023
## 54 1090.11628 2084.3023
## 55 1090.11628 2084.3023
## 56 1090.11628 2084.3023
## 57 1090.11628 2084.3023
## 58 1090.11628 2084.3023
## 59 1090.11628 2084.3023
## 60 1090.11628 2084.3023
## 61 1090.11628 2084.3023
## 62 1090.11628 2084.3023
## 63 1090.11628 2084.3023
## 64 1090.11628 2084.3023
## 65 1090.11628 2084.3023
## 66 1090.11628 2084.3023
## 67 1090.11628 2084.3023
## 68 1090.11628 2084.3023
## 69 1090.11628 2084.3023
## 70 1090.11628 2084.3023
## 71 1090.11628 2084.3023
## 72 1090.11628 2084.3023
## 73 2180.23256 2947.6744
## 74 2180.23256 2947.6744
## 75 2180.23256 2947.6744
## 76 2180.23256 2947.6744
## 77 2180.23256 2947.6744
## 78 2180.23256 2947.6744
## 79 2180.23256 2947.6744
## 80 2180.23256 2947.6744
## 81 2180.23256 2947.6744
## 82 2180.23256 2947.6744
## 83 2180.23256 2947.6744
## 84 2180.23256 2947.6744
## 85 2180.23256 2947.6744
## 86 2180.23256 2947.6744
## 87 2180.23256 2947.6744
## 88 2180.23256 2947.6744
## 89 2180.23256 2947.6744
## 90 2180.23256 2947.6744
## 91 2180.23256 2947.6744
## 92 2180.23256 2947.6744
## 93 2180.23256 2947.6744
## 94 2180.23256 2947.6744
## 95 2180.23256 2947.6744
## 96 2180.23256 2947.6744
## 97 549.41860 1308.1395
## 98 549.41860 1308.1395
## 99 549.41860 1308.1395
## 100 549.41860 1308.1395
## 101 549.41860 1308.1395
## 102 549.41860 1308.1395
## 103 549.41860 1308.1395
## 104 549.41860 1308.1395
## 105 549.41860 1308.1395
## 106 549.41860 1308.1395
## 107 549.41860 1308.1395
## 108 549.41860 1308.1395
## 109 549.41860 1308.1395
## 110 549.41860 1308.1395
## 111 549.41860 1308.1395
## 112 549.41860 1308.1395
## 113 549.41860 1308.1395
## 114 549.41860 1308.1395
## 115 549.41860 1308.1395
## 116 549.41860 1308.1395
## 117 549.41860 1308.1395
## 118 549.41860 1308.1395
## 119 549.41860 1308.1395
## 120 549.41860 1308.1395
## 121 0.00000 767.4419
## 122 0.00000 767.4419
## 123 0.00000 767.4419
## 124 0.00000 767.4419
## 125 0.00000 767.4419
## 126 0.00000 767.4419
## 127 0.00000 767.4419
## 128 0.00000 767.4419
## 129 0.00000 767.4419
## 130 0.00000 767.4419
## 131 0.00000 767.4419
## 132 0.00000 767.4419
## 133 0.00000 767.4419
## 134 0.00000 767.4419
## 135 0.00000 767.4419
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## 140 0.00000 767.4419
## 141 0.00000 767.4419
## 142 0.00000 767.4419
## 143 0.00000 767.4419
## 144 0.00000 767.4419
## 145 31.39535 1460.7558
## 146 31.39535 1460.7558
## 147 31.39535 1460.7558
## 148 31.39535 1460.7558
## 149 31.39535 1460.7558
## 150 31.39535 1460.7558
## 151 31.39535 1460.7558
## 152 31.39535 1460.7558
## 153 31.39535 1460.7558
## 154 31.39535 1460.7558
## 155 31.39535 1460.7558
## 156 31.39535 1460.7558
## 157 31.39535 1460.7558
## 158 31.39535 1460.7558
## 159 31.39535 1460.7558
## 160 31.39535 1460.7558
## 161 31.39535 1460.7558
## 162 31.39535 1460.7558
## 163 31.39535 1460.7558
## 164 31.39535 1460.7558
## 165 31.39535 1460.7558
## 166 31.39535 1460.7558
## 167 31.39535 1460.7558
## 168 31.39535 1460.7558
## 169 126.45349 187.5000
## 170 126.45349 187.5000
## 171 126.45349 187.5000
## 172 126.45349 187.5000
## 173 126.45349 187.5000
## 174 126.45349 187.5000
## 175 126.45349 187.5000
## 176 126.45349 187.5000
## 177 126.45349 187.5000
## 178 126.45349 187.5000
## 179 126.45349 187.5000
## 180 126.45349 187.5000
## 181 126.45349 187.5000
## 182 126.45349 187.5000
## 183 126.45349 187.5000
## 184 126.45349 187.5000
## 185 126.45349 187.5000
## 186 126.45349 187.5000
## 187 126.45349 187.5000
## 188 126.45349 187.5000
## 189 126.45349 187.5000
## 190 126.45349 187.5000
## 191 126.45349 187.5000
## 192 126.45349 187.5000
## 193 635.75581 981.9767
## 194 635.75581 981.9767
## 195 635.75581 981.9767
## 196 635.75581 981.9767
## 197 635.75581 981.9767
## 198 635.75581 981.9767
## 199 635.75581 981.9767
## 200 635.75581 981.9767
## 201 635.75581 981.9767
## 202 635.75581 981.9767
## 203 635.75581 981.9767
## 204 635.75581 981.9767
## 205 635.75581 981.9767
## 206 635.75581 981.9767
## 207 635.75581 981.9767
## 208 635.75581 981.9767
## 209 635.75581 981.9767
## 210 635.75581 981.9767
## 211 635.75581 981.9767
## 212 635.75581 981.9767
## 213 635.75581 981.9767
## 214 635.75581 981.9767
## 215 635.75581 981.9767
## 216 635.75581 981.9767
## 217 1029.06977 0.0000
## 218 1029.06977 0.0000
## 219 1029.06977 0.0000
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## 221 1029.06977 0.0000
## 222 1029.06977 0.0000
## 223 1029.06977 0.0000
## 224 1029.06977 0.0000
## 225 1029.06977 0.0000
## 226 1029.06977 0.0000
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## 231 1029.06977 0.0000
## 232 1029.06977 0.0000
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## 235 1029.06977 0.0000
## 236 1029.06977 0.0000
## 237 1029.06977 0.0000
## 238 1029.06977 0.0000
## 239 1029.06977 0.0000
## 240 1029.06977 0.0000
## 241 0.00000 1997.0930
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## 251 0.00000 1997.0930
## 252 0.00000 1997.0930
## 253 0.00000 1997.0930
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## 256 0.00000 1997.0930
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## 264 0.00000 1997.0930
## 265 2188.95349 3122.0930
## 266 2188.95349 3122.0930
## 267 2188.95349 3122.0930
## 268 2188.95349 3122.0930
## 269 2188.95349 3122.0930
## 270 2188.95349 3122.0930
## 271 2188.95349 3122.0930
## 272 2188.95349 3122.0930
## 273 2188.95349 3122.0930
## 274 2188.95349 3122.0930
## 275 2188.95349 3122.0930
## 276 2188.95349 3122.0930
## 277 2188.95349 3122.0930
## 278 2188.95349 3122.0930
## 279 2188.95349 3122.0930
## 280 2188.95349 3122.0930
## 281 2188.95349 3122.0930
## 282 2188.95349 3122.0930
## 283 2188.95349 3122.0930
## 284 2188.95349 3122.0930
## 285 2188.95349 3122.0930
## 286 2188.95349 3122.0930
## 287 2188.95349 3122.0930
## 288 2188.95349 3122.0930
## 289 3654.06977 218.0233
## 290 3654.06977 218.0233
## 291 3654.06977 218.0233
## 292 3654.06977 218.0233
## 293 3654.06977 218.0233
## 294 3654.06977 218.0233
## 295 3654.06977 218.0233
## 296 3654.06977 218.0233
## 297 3654.06977 218.0233
## 298 3654.06977 218.0233
## 299 3654.06977 218.0233
## 300 3654.06977 218.0233
## 301 3654.06977 218.0233
## 302 3654.06977 218.0233
## 303 3654.06977 218.0233
## 304 3654.06977 218.0233
## 305 3654.06977 218.0233
## 306 3654.06977 218.0233
## 307 3654.06977 218.0233
## 308 3654.06977 218.0233
## 309 3654.06977 218.0233
## 310 3654.06977 218.0233
## 311 3654.06977 218.0233
## 312 3654.06977 218.0233
## 313 287.79070 3270.3488
## 314 287.79070 3270.3488
## 315 287.79070 3270.3488
## 316 287.79070 3270.3488
## 317 287.79070 3270.3488
## 318 287.79070 3270.3488
## 319 287.79070 3270.3488
## 320 287.79070 3270.3488
## 321 287.79070 3270.3488
## 322 287.79070 3270.3488
## 323 287.79070 3270.3488
## 324 287.79070 3270.3488
## 325 287.79070 3270.3488
## 326 287.79070 3270.3488
## 327 287.79070 3270.3488
## 328 287.79070 3270.3488
## 329 287.79070 3270.3488
## 330 287.79070 3270.3488
## 331 287.79070 3270.3488
## 332 287.79070 3270.3488
## 333 287.79070 3270.3488
## 334 287.79070 3270.3488
## 335 287.79070 3270.3488
## 336 287.79070 3270.3488
## 337 31.39535 218.0233
## 338 31.39535 218.0233
## 339 31.39535 218.0233
## 340 31.39535 218.0233
## 341 31.39535 218.0233
## 342 31.39535 218.0233
## 343 31.39535 218.0233
## 344 31.39535 218.0233
## 345 31.39535 218.0233
## 346 31.39535 218.0233
## 347 31.39535 218.0233
## 348 31.39535 218.0233
## 349 31.39535 218.0233
## 350 31.39535 218.0233
## 351 31.39535 218.0233
## 352 31.39535 218.0233
## 353 31.39535 218.0233
## 354 31.39535 218.0233
## 355 31.39535 218.0233
## 356 31.39535 218.0233
## 357 31.39535 218.0233
## 358 31.39535 218.0233
## 359 31.39535 218.0233
## 360 31.39535 218.0233
## 361 0.00000 928.7791
## 362 0.00000 928.7791
## 363 0.00000 928.7791
## 364 0.00000 928.7791
## 365 0.00000 928.7791
## 366 0.00000 928.7791
## 367 0.00000 928.7791
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## 369 0.00000 928.7791
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## 373 0.00000 928.7791
## 374 0.00000 928.7791
## 375 0.00000 928.7791
## 376 0.00000 928.7791
## 377 0.00000 928.7791
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## 379 0.00000 928.7791
## 380 0.00000 928.7791
## 381 0.00000 928.7791
## 382 0.00000 928.7791
## 383 0.00000 928.7791
## 384 0.00000 928.7791
## 385 635.75581 981.9767
## 386 635.75581 981.9767
## 387 635.75581 981.9767
## 388 635.75581 981.9767
## 389 635.75581 981.9767
## 390 635.75581 981.9767
## 391 635.75581 981.9767
## 392 635.75581 981.9767
## 393 635.75581 981.9767
## 394 635.75581 981.9767
## 395 635.75581 981.9767
## 396 635.75581 981.9767
## 397 635.75581 981.9767
## 398 635.75581 981.9767
## 399 635.75581 981.9767
## 400 635.75581 981.9767
## 401 635.75581 981.9767
## 402 635.75581 981.9767
## 403 635.75581 981.9767
## 404 635.75581 981.9767
## 405 635.75581 981.9767
## 406 635.75581 981.9767
## 407 635.75581 981.9767
## 408 635.75581 981.9767
## 409 2162.79070 2825.5814
## 410 2162.79070 2825.5814
## 411 2162.79070 2825.5814
## 412 2162.79070 2825.5814
## 413 2162.79070 2825.5814
## 414 2162.79070 2825.5814
## 415 2162.79070 2825.5814
## 416 2162.79070 2825.5814
## 417 2162.79070 2825.5814
## 418 2162.79070 2825.5814
## 419 2162.79070 2825.5814
## 420 2162.79070 2825.5814
## 421 2162.79070 2825.5814
## 422 2162.79070 2825.5814
## 423 2162.79070 2825.5814
## 424 2162.79070 2825.5814
## 425 2162.79070 2825.5814
## 426 2162.79070 2825.5814
## 427 2162.79070 2825.5814
## 428 2162.79070 2825.5814
## 429 2162.79070 2825.5814
## 430 2162.79070 2825.5814
## 431 2162.79070 2825.5814
## 432 2162.79070 2825.5814
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## 435 1090.11628 3174.4186
## 436 1090.11628 3174.4186
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## 439 1090.11628 3174.4186
## 440 1090.11628 3174.4186
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## 442 1090.11628 3174.4186
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## 447 1090.11628 3174.4186
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## 451 1090.11628 3174.4186
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## 454 1090.11628 3174.4186
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## 485 2215.11628 2433.1395
## 486 2215.11628 2433.1395
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## 488 2215.11628 2433.1395
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## 492 2215.11628 2433.1395
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## 500 2215.11628 2433.1395
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## 2999 549.41860 1090.1163
## 3000 549.41860 1090.1163
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## 3049 126.45349 187.5000
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## 3068 126.45349 187.5000
## 3069 126.45349 187.5000
## 3070 126.45349 187.5000
## 3071 126.45349 187.5000
## 3072 126.45349 187.5000
## 3073 635.75581 981.9767
## 3074 635.75581 981.9767
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## 3077 635.75581 981.9767
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## 3093 635.75581 981.9767
## 3094 635.75581 981.9767
## 3095 635.75581 981.9767
## 3096 635.75581 981.9767
## 3097 1029.06977 418.6047
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## 3120 1029.06977 418.6047
## 3121 0.00000 1220.9302
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## 3165 2188.95349 3122.0930
## 3166 2188.95349 3122.0930
## 3167 2188.95349 3122.0930
## 3168 2188.95349 3122.0930
## 3169 3654.06977 0.0000
## 3170 3654.06977 0.0000
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## 3173 3654.06977 0.0000
## 3174 3654.06977 0.0000
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## 3189 3654.06977 0.0000
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## 3191 3654.06977 0.0000
## 3192 3654.06977 0.0000
## 3193 287.79070 3270.3488
## 3194 287.79070 3270.3488
## 3195 287.79070 3270.3488
## 3196 287.79070 3270.3488
## 3197 287.79070 3270.3488
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## 3210 287.79070 3270.3488
## 3211 287.79070 3270.3488
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## 3213 287.79070 3270.3488
## 3214 287.79070 3270.3488
## 3215 287.79070 3270.3488
## 3216 287.79070 3270.3488
## 3217 0.00000 109.0116
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## 3223 0.00000 109.0116
## 3224 0.00000 109.0116
## 3225 0.00000 109.0116
## total_metaecosystem_Tet_indiv connection ecosystem_size_symmetry set
## 1 2243.895 unconnected asymmetric 1
## 2 2243.895 unconnected asymmetric 2
## 3 2243.895 unconnected asymmetric 3
## 4 2243.895 unconnected asymmetric 4
## 5 2243.895 unconnected asymmetric 7
## 6 2243.895 unconnected asymmetric 8
## 7 2243.895 unconnected asymmetric 9
## 8 2243.895 unconnected asymmetric 10
## 9 2243.895 unconnected asymmetric 11
## 10 2243.895 unconnected asymmetric 12
## 11 2243.895 unconnected asymmetric 13
## 12 2243.895 unconnected asymmetric 14
## 13 2243.895 unconnected asymmetric 27
## 14 2243.895 unconnected asymmetric 28
## 15 2243.895 unconnected asymmetric 29
## 16 2243.895 unconnected asymmetric 30
## 17 2243.895 unconnected asymmetric 31
## 18 2243.895 unconnected asymmetric 32
## 19 2243.895 unconnected asymmetric 33
## 20 2243.895 unconnected asymmetric 34
## 21 2243.895 unconnected asymmetric 37
## 22 2243.895 unconnected asymmetric 38
## 23 2243.895 unconnected asymmetric 39
## 24 2243.895 unconnected asymmetric 40
## 25 0.000 unconnected asymmetric 1
## 26 0.000 unconnected asymmetric 2
## 27 0.000 unconnected asymmetric 3
## 28 0.000 unconnected asymmetric 4
## 29 0.000 unconnected asymmetric 7
## 30 0.000 unconnected asymmetric 8
## 31 0.000 unconnected asymmetric 9
## 32 0.000 unconnected asymmetric 10
## 33 0.000 unconnected asymmetric 11
## 34 0.000 unconnected asymmetric 12
## 35 0.000 unconnected asymmetric 13
## 36 0.000 unconnected asymmetric 14
## 37 0.000 unconnected asymmetric 27
## 38 0.000 unconnected asymmetric 28
## 39 0.000 unconnected asymmetric 29
## 40 0.000 unconnected asymmetric 30
## 41 0.000 unconnected asymmetric 31
## 42 0.000 unconnected asymmetric 32
## 43 0.000 unconnected asymmetric 33
## 44 0.000 unconnected asymmetric 34
## 45 0.000 unconnected asymmetric 37
## 46 0.000 unconnected asymmetric 38
## 47 0.000 unconnected asymmetric 39
## 48 0.000 unconnected asymmetric 40
## 49 0.000 unconnected asymmetric 1
## 50 0.000 unconnected asymmetric 2
## 51 0.000 unconnected asymmetric 3
## 52 0.000 unconnected asymmetric 4
## 53 0.000 unconnected asymmetric 7
## 54 0.000 unconnected asymmetric 8
## 55 0.000 unconnected asymmetric 9
## 56 0.000 unconnected asymmetric 10
## 57 0.000 unconnected asymmetric 11
## 58 0.000 unconnected asymmetric 12
## 59 0.000 unconnected asymmetric 13
## 60 0.000 unconnected asymmetric 14
## 61 0.000 unconnected asymmetric 27
## 62 0.000 unconnected asymmetric 28
## 63 0.000 unconnected asymmetric 29
## 64 0.000 unconnected asymmetric 30
## 65 0.000 unconnected asymmetric 31
## 66 0.000 unconnected asymmetric 32
## 67 0.000 unconnected asymmetric 33
## 68 0.000 unconnected asymmetric 34
## 69 0.000 unconnected asymmetric 37
## 70 0.000 unconnected asymmetric 38
## 71 0.000 unconnected asymmetric 39
## 72 0.000 unconnected asymmetric 40
## 73 0.000 unconnected asymmetric 1
## 74 0.000 unconnected asymmetric 2
## 75 0.000 unconnected asymmetric 3
## 76 0.000 unconnected asymmetric 4
## 77 0.000 unconnected asymmetric 7
## 78 0.000 unconnected asymmetric 8
## 79 0.000 unconnected asymmetric 9
## 80 0.000 unconnected asymmetric 10
## 81 0.000 unconnected asymmetric 11
## 82 0.000 unconnected asymmetric 12
## 83 0.000 unconnected asymmetric 13
## 84 0.000 unconnected asymmetric 14
## 85 0.000 unconnected asymmetric 27
## 86 0.000 unconnected asymmetric 28
## 87 0.000 unconnected asymmetric 29
## 88 0.000 unconnected asymmetric 30
## 89 0.000 unconnected asymmetric 31
## 90 0.000 unconnected asymmetric 32
## 91 0.000 unconnected asymmetric 33
## 92 0.000 unconnected asymmetric 34
## 93 0.000 unconnected asymmetric 37
## 94 0.000 unconnected asymmetric 38
## 95 0.000 unconnected asymmetric 39
## 96 0.000 unconnected asymmetric 40
## 97 0.000 unconnected asymmetric 1
## 98 0.000 unconnected asymmetric 2
## 99 0.000 unconnected asymmetric 3
## 100 0.000 unconnected asymmetric 4
## 101 0.000 unconnected asymmetric 7
## 102 0.000 unconnected asymmetric 8
## 103 0.000 unconnected asymmetric 9
## 104 0.000 unconnected asymmetric 10
## 105 0.000 unconnected asymmetric 11
## 106 0.000 unconnected asymmetric 12
## 107 0.000 unconnected asymmetric 13
## 108 0.000 unconnected asymmetric 14
## 109 0.000 unconnected asymmetric 27
## 110 0.000 unconnected asymmetric 28
## 111 0.000 unconnected asymmetric 29
## 112 0.000 unconnected asymmetric 30
## 113 0.000 unconnected asymmetric 31
## 114 0.000 unconnected asymmetric 32
## 115 0.000 unconnected asymmetric 33
## 116 0.000 unconnected asymmetric 34
## 117 0.000 unconnected asymmetric 37
## 118 0.000 unconnected asymmetric 38
## 119 0.000 unconnected asymmetric 39
## 120 0.000 unconnected asymmetric 40
## 121 0.000 unconnected asymmetric 1
## 122 0.000 unconnected asymmetric 2
## 123 0.000 unconnected asymmetric 3
## 124 0.000 unconnected asymmetric 4
## 125 0.000 unconnected asymmetric 7
## 126 0.000 unconnected asymmetric 8
## 127 0.000 unconnected asymmetric 9
## 128 0.000 unconnected asymmetric 10
## 129 0.000 unconnected asymmetric 11
## 130 0.000 unconnected asymmetric 12
## 131 0.000 unconnected asymmetric 13
## 132 0.000 unconnected asymmetric 14
## 133 0.000 unconnected asymmetric 27
## 134 0.000 unconnected asymmetric 28
## 135 0.000 unconnected asymmetric 29
## 136 0.000 unconnected asymmetric 30
## 137 0.000 unconnected asymmetric 31
## 138 0.000 unconnected asymmetric 32
## 139 0.000 unconnected asymmetric 33
## 140 0.000 unconnected asymmetric 34
## 141 0.000 unconnected asymmetric 37
## 142 0.000 unconnected asymmetric 38
## 143 0.000 unconnected asymmetric 39
## 144 0.000 unconnected asymmetric 40
## 145 0.000 unconnected asymmetric 1
## 146 0.000 unconnected asymmetric 2
## 147 0.000 unconnected asymmetric 3
## 148 0.000 unconnected asymmetric 4
## 149 0.000 unconnected asymmetric 7
## 150 0.000 unconnected asymmetric 8
## 151 0.000 unconnected asymmetric 9
## 152 0.000 unconnected asymmetric 10
## 153 0.000 unconnected asymmetric 11
## 154 0.000 unconnected asymmetric 12
## 155 0.000 unconnected asymmetric 13
## 156 0.000 unconnected asymmetric 14
## 157 0.000 unconnected asymmetric 27
## 158 0.000 unconnected asymmetric 28
## 159 0.000 unconnected asymmetric 29
## 160 0.000 unconnected asymmetric 30
## 161 0.000 unconnected asymmetric 31
## 162 0.000 unconnected asymmetric 32
## 163 0.000 unconnected asymmetric 33
## 164 0.000 unconnected asymmetric 34
## 165 0.000 unconnected asymmetric 37
## 166 0.000 unconnected asymmetric 38
## 167 0.000 unconnected asymmetric 39
## 168 0.000 unconnected asymmetric 40
## 169 0.000 unconnected asymmetric 1
## 170 0.000 unconnected asymmetric 2
## 171 0.000 unconnected asymmetric 3
## 172 0.000 unconnected asymmetric 4
## 173 0.000 unconnected asymmetric 7
## 174 0.000 unconnected asymmetric 8
## 175 0.000 unconnected asymmetric 9
## 176 0.000 unconnected asymmetric 10
## 177 0.000 unconnected asymmetric 11
## 178 0.000 unconnected asymmetric 12
## 179 0.000 unconnected asymmetric 13
## 180 0.000 unconnected asymmetric 14
## 181 0.000 unconnected asymmetric 27
## 182 0.000 unconnected asymmetric 28
## 183 0.000 unconnected asymmetric 29
## 184 0.000 unconnected asymmetric 30
## 185 0.000 unconnected asymmetric 31
## 186 0.000 unconnected asymmetric 32
## 187 0.000 unconnected asymmetric 33
## 188 0.000 unconnected asymmetric 34
## 189 0.000 unconnected asymmetric 37
## 190 0.000 unconnected asymmetric 38
## 191 0.000 unconnected asymmetric 39
## 192 0.000 unconnected asymmetric 40
## 193 2243.895 unconnected asymmetric 81
## 194 2243.895 unconnected asymmetric 82
## 195 2243.895 unconnected asymmetric 83
## 196 2243.895 unconnected asymmetric 84
## 197 2243.895 unconnected asymmetric 87
## 198 2243.895 unconnected asymmetric 88
## 199 2243.895 unconnected asymmetric 89
## 200 2243.895 unconnected asymmetric 90
## 201 2243.895 unconnected asymmetric 91
## 202 2243.895 unconnected asymmetric 92
## 203 2243.895 unconnected asymmetric 93
## 204 2243.895 unconnected asymmetric 94
## 205 2243.895 unconnected asymmetric 107
## 206 2243.895 unconnected asymmetric 108
## 207 2243.895 unconnected asymmetric 109
## 208 2243.895 unconnected asymmetric 110
## 209 2243.895 unconnected asymmetric 111
## 210 2243.895 unconnected asymmetric 112
## 211 2243.895 unconnected asymmetric 113
## 212 2243.895 unconnected asymmetric 114
## 213 2243.895 unconnected asymmetric 117
## 214 2243.895 unconnected asymmetric 118
## 215 2243.895 unconnected asymmetric 119
## 216 2243.895 unconnected asymmetric 120
## 217 0.000 unconnected asymmetric 81
## 218 0.000 unconnected asymmetric 82
## 219 0.000 unconnected asymmetric 83
## 220 0.000 unconnected asymmetric 84
## 221 0.000 unconnected asymmetric 87
## 222 0.000 unconnected asymmetric 88
## 223 0.000 unconnected asymmetric 89
## 224 0.000 unconnected asymmetric 90
## 225 0.000 unconnected asymmetric 91
## 226 0.000 unconnected asymmetric 92
## 227 0.000 unconnected asymmetric 93
## 228 0.000 unconnected asymmetric 94
## 229 0.000 unconnected asymmetric 107
## 230 0.000 unconnected asymmetric 108
## 231 0.000 unconnected asymmetric 109
## 232 0.000 unconnected asymmetric 110
## 233 0.000 unconnected asymmetric 111
## 234 0.000 unconnected asymmetric 112
## 235 0.000 unconnected asymmetric 113
## 236 0.000 unconnected asymmetric 114
## 237 0.000 unconnected asymmetric 117
## 238 0.000 unconnected asymmetric 118
## 239 0.000 unconnected asymmetric 119
## 240 0.000 unconnected asymmetric 120
## 241 0.000 unconnected asymmetric 81
## 242 0.000 unconnected asymmetric 82
## 243 0.000 unconnected asymmetric 83
## 244 0.000 unconnected asymmetric 84
## 245 0.000 unconnected asymmetric 87
## 246 0.000 unconnected asymmetric 88
## 247 0.000 unconnected asymmetric 89
## 248 0.000 unconnected asymmetric 90
## 249 0.000 unconnected asymmetric 91
## 250 0.000 unconnected asymmetric 92
## 251 0.000 unconnected asymmetric 93
## 252 0.000 unconnected asymmetric 94
## 253 0.000 unconnected asymmetric 107
## 254 0.000 unconnected asymmetric 108
## 255 0.000 unconnected asymmetric 109
## 256 0.000 unconnected asymmetric 110
## 257 0.000 unconnected asymmetric 111
## 258 0.000 unconnected asymmetric 112
## 259 0.000 unconnected asymmetric 113
## 260 0.000 unconnected asymmetric 114
## 261 0.000 unconnected asymmetric 117
## 262 0.000 unconnected asymmetric 118
## 263 0.000 unconnected asymmetric 119
## 264 0.000 unconnected asymmetric 120
## 265 0.000 unconnected asymmetric 81
## 266 0.000 unconnected asymmetric 82
## 267 0.000 unconnected asymmetric 83
## 268 0.000 unconnected asymmetric 84
## 269 0.000 unconnected asymmetric 87
## 270 0.000 unconnected asymmetric 88
## 271 0.000 unconnected asymmetric 89
## 272 0.000 unconnected asymmetric 90
## 273 0.000 unconnected asymmetric 91
## 274 0.000 unconnected asymmetric 92
## 275 0.000 unconnected asymmetric 93
## 276 0.000 unconnected asymmetric 94
## 277 0.000 unconnected asymmetric 107
## 278 0.000 unconnected asymmetric 108
## 279 0.000 unconnected asymmetric 109
## 280 0.000 unconnected asymmetric 110
## 281 0.000 unconnected asymmetric 111
## 282 0.000 unconnected asymmetric 112
## 283 0.000 unconnected asymmetric 113
## 284 0.000 unconnected asymmetric 114
## 285 0.000 unconnected asymmetric 117
## 286 0.000 unconnected asymmetric 118
## 287 0.000 unconnected asymmetric 119
## 288 0.000 unconnected asymmetric 120
## 289 0.000 unconnected asymmetric 81
## 290 0.000 unconnected asymmetric 82
## 291 0.000 unconnected asymmetric 83
## 292 0.000 unconnected asymmetric 84
## 293 0.000 unconnected asymmetric 87
## 294 0.000 unconnected asymmetric 88
## 295 0.000 unconnected asymmetric 89
## 296 0.000 unconnected asymmetric 90
## 297 0.000 unconnected asymmetric 91
## 298 0.000 unconnected asymmetric 92
## 299 0.000 unconnected asymmetric 93
## 300 0.000 unconnected asymmetric 94
## 301 0.000 unconnected asymmetric 107
## 302 0.000 unconnected asymmetric 108
## 303 0.000 unconnected asymmetric 109
## 304 0.000 unconnected asymmetric 110
## 305 0.000 unconnected asymmetric 111
## 306 0.000 unconnected asymmetric 112
## 307 0.000 unconnected asymmetric 113
## 308 0.000 unconnected asymmetric 114
## 309 0.000 unconnected asymmetric 117
## 310 0.000 unconnected asymmetric 118
## 311 0.000 unconnected asymmetric 119
## 312 0.000 unconnected asymmetric 120
## 313 0.000 unconnected asymmetric 81
## 314 0.000 unconnected asymmetric 82
## 315 0.000 unconnected asymmetric 83
## 316 0.000 unconnected asymmetric 84
## 317 0.000 unconnected asymmetric 87
## 318 0.000 unconnected asymmetric 88
## 319 0.000 unconnected asymmetric 89
## 320 0.000 unconnected asymmetric 90
## 321 0.000 unconnected asymmetric 91
## 322 0.000 unconnected asymmetric 92
## 323 0.000 unconnected asymmetric 93
## 324 0.000 unconnected asymmetric 94
## 325 0.000 unconnected asymmetric 107
## 326 0.000 unconnected asymmetric 108
## 327 0.000 unconnected asymmetric 109
## 328 0.000 unconnected asymmetric 110
## 329 0.000 unconnected asymmetric 111
## 330 0.000 unconnected asymmetric 112
## 331 0.000 unconnected asymmetric 113
## 332 0.000 unconnected asymmetric 114
## 333 0.000 unconnected asymmetric 117
## 334 0.000 unconnected asymmetric 118
## 335 0.000 unconnected asymmetric 119
## 336 0.000 unconnected asymmetric 120
## 337 0.000 unconnected asymmetric 81
## 338 0.000 unconnected asymmetric 82
## 339 0.000 unconnected asymmetric 83
## 340 0.000 unconnected asymmetric 84
## 341 0.000 unconnected asymmetric 87
## 342 0.000 unconnected asymmetric 88
## 343 0.000 unconnected asymmetric 89
## 344 0.000 unconnected asymmetric 90
## 345 0.000 unconnected asymmetric 91
## 346 0.000 unconnected asymmetric 92
## 347 0.000 unconnected asymmetric 93
## 348 0.000 unconnected asymmetric 94
## 349 0.000 unconnected asymmetric 107
## 350 0.000 unconnected asymmetric 108
## 351 0.000 unconnected asymmetric 109
## 352 0.000 unconnected asymmetric 110
## 353 0.000 unconnected asymmetric 111
## 354 0.000 unconnected asymmetric 112
## 355 0.000 unconnected asymmetric 113
## 356 0.000 unconnected asymmetric 114
## 357 0.000 unconnected asymmetric 117
## 358 0.000 unconnected asymmetric 118
## 359 0.000 unconnected asymmetric 119
## 360 0.000 unconnected asymmetric 120
## 361 0.000 unconnected asymmetric 81
## 362 0.000 unconnected asymmetric 82
## 363 0.000 unconnected asymmetric 83
## 364 0.000 unconnected asymmetric 84
## 365 0.000 unconnected asymmetric 87
## 366 0.000 unconnected asymmetric 88
## 367 0.000 unconnected asymmetric 89
## 368 0.000 unconnected asymmetric 90
## 369 0.000 unconnected asymmetric 91
## 370 0.000 unconnected asymmetric 92
## 371 0.000 unconnected asymmetric 93
## 372 0.000 unconnected asymmetric 94
## 373 0.000 unconnected asymmetric 107
## 374 0.000 unconnected asymmetric 108
## 375 0.000 unconnected asymmetric 109
## 376 0.000 unconnected asymmetric 110
## 377 0.000 unconnected asymmetric 111
## 378 0.000 unconnected asymmetric 112
## 379 0.000 unconnected asymmetric 113
## 380 0.000 unconnected asymmetric 114
## 381 0.000 unconnected asymmetric 117
## 382 0.000 unconnected asymmetric 118
## 383 0.000 unconnected asymmetric 119
## 384 0.000 unconnected asymmetric 120
## 385 2243.895 unconnected asymmetric 41
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## ID_first_ecosystem ID_second_ecosystem
## 1 1 11
## 2 1 11
## 3 1 11
## 4 1 11
## 5 1 11
## 6 1 11
## 7 1 11
## 8 1 11
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## 10 1 11
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## [ reached 'max' / getOption("max.print") -- omitted 6695 rows ]ds_metaecosystems <- ds_metaecosystems %>%
mutate(
type = case_when(
metaecosystem_type == "Small-Large unconnected" ~ "asymmetric",
metaecosystem_type == "Small-Large meta-ecosystem" ~ "asymmetric",
metaecosystem_type == "Medium-Medium unconnected" ~ "symmetric",
metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "symmetric",
metaecosystem_type == "Small-Small meta-ecosystem" ~ "Small-Small",
metaecosystem_type == "Medium-Medium meta-ecosystem" ~ "Medium-Medium"
))Filter according to disturbance
Here I’m filtering ecosystems to have only the ones with disturbance high.
#Filter data sets according to the global disturbance
ds_individuals = ds_individuals %>%
filter(disturbance == disturbance_global_input)
ds_ecosystems = ds_ecosystems %>%
filter(disturbance == disturbance_global_input)
ds_ecosystems_effect_size = ds_ecosystems_effect_size %>%
filter(disturbance == disturbance_global_input)
ds_metaecosystems = ds_metaecosystems %>%
filter(disturbance == disturbance_global_input)ds_classes = ds_classes %>%
filter(disturbance == disturbance_global_input)
ds_classes_effect_size = ds_classes_effect_size %>%
filter(disturbance == disturbance_global_input)Plots & Analysis
All Meta-ecosystems
metaecosystem_type_i = c("Small-Small meta-ecosystem",
"Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Large-Large meta-ecosystem",
"Small-Large meta-ecosystem",
"Small-Large unconnected")Alpha (mean Shannon)
response_variable = "mean_shannon"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)
Beta (Bray-Curtis)
response_variable = "bray_curtis"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)## Warning: Removed 2 rows containing non-finite outside the scale range
## (`stat_summary()`).
Gamma (regional richness)
response_variable = "metaecosystem_richness"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)
Biomass
response_variable = "total_metaecosystem_bioarea_mm2"Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)
SL vs MM
Alpha (mean Shannon)
response_variable = "mean_shannon"metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Small-Large meta-ecosystem",
"Small-Large unconnected")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.
SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
"Small-Large unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.2e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+02## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+02## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.2e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.7e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.0e-02## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.4e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.2e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.1e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.1e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.2e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.1e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -7.2e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.3e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.7e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.6e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.4e-01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.8e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.9e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.3e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.3e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.3e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00482332 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.1e-01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.3e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.5e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -7.5e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.9e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.6e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e-01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.2e+02## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.6e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.1e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.1e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.1e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.9e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -8.6e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.4e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.8e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e-01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.1e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.6e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0147445 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.4e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -7.0e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.3e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.8e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.7 0.061 * weakClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1030 1031 1037 1044 -3.2658662
## 2 1030 1031 1039 1042 -3.1902927
## 3 1026 1035 1037 1044 -3.1184539
## 4 1026 1035 1039 1042 -3.0498505
## 5 1029 1031 1040 1042 -2.9582525
## 6 1027 1031 1040 1044 -2.9161783
## 7 1029 1035 1036 1042 -2.8370408
## 8 1027 1035 1036 1044 -2.7773951
## 9 1026 1034 1040 1042 -2.7516252
## 10 1029 1031 1037 1045 -2.7318940
## 11 1030 1033 1037 1044 -2.7253151
## 12 1030 1034 1036 1042 -2.7137428
## 13 1030 1032 1036 1044 -2.7114029
## 14 1027 1031 1039 1045 -2.6823829
## 15 1030 1033 1039 1042 -2.6125976
## 16 1026 1032 1040 1044 -2.6074367
## 17 1028 1035 1037 1044 -2.5148704
## 18 1026 1033 1037 1044 -2.5148462
## 19 1026 1034 1037 1045 -2.5107510
## 20 1026 1032 1039 1045 -2.4777456
## 21 1028 1031 1037 1044 -2.4644361
## 22 1028 1035 1039 1042 -2.3997450
## 23 1029 1033 1040 1042 -2.3883546
## 24 1027 1033 1040 1044 -2.3422727
## 25 1026 1033 1039 1042 -2.3223480
## 26 1029 1035 1037 1041 -2.2911892
## 27 1028 1031 1039 1042 -2.2608060
## 28 1029 1033 1037 1045 -2.2388491
## 29 1027 1035 1039 1041 -2.2329835
## 30 1030 1034 1037 1041 -2.1858149
## 31 1030 1033 1036 1044 -2.1815047
## 32 1030 1032 1039 1041 -2.1812818
## 33 1029 1032 1036 1045 -2.1666678
## 34 1027 1034 1036 1045 -2.1360380
## 35 1027 1033 1036 1044 -2.1353277
## 36 1027 1033 1039 1045 -2.1347409
## 37 1028 1032 1040 1044 -2.1315380
## 38 1028 1034 1040 1042 -2.1114067
## 39 1029 1033 1036 1042 -2.1107839
## 40 1026 1033 1040 1044 -2.0926051
## 41 1029 1035 1038 1042 -2.0353298
## 42 1028 1031 1040 1044 -2.0241523
## 43 1028 1035 1036 1044 -1.9870485
## 44 1028 1032 1036 1044 -1.9830983
## 45 1028 1034 1037 1045 -1.9598801
## 46 1026 1033 1039 1045 -1.9486814
## 47 1029 1032 1040 1041 -1.9381692
## 48 1027 1035 1038 1044 -1.9306806
## 49 1030 1032 1038 1044 -1.9295017
## 50 1030 1034 1038 1042 -1.9220500
## 51 1028 1032 1039 1045 -1.9218019
## 52 1030 1031 1038 1044 -1.9169879
## 53 1027 1034 1040 1041 -1.9074780
## 54 1028 1031 1039 1045 -1.8794146
## 55 1027 1031 1038 1044 -1.8782998
## 56 1029 1031 1038 1042 -1.8673505
## 57 1028 1034 1036 1042 -1.8480452
## 58 1026 1035 1038 1044 -1.8019937
## 59 1029 1033 1037 1041 -1.7843168
## 60 1026 1032 1038 1044 -1.7648774
## 61 1030 1033 1039 1041 -1.7338144
## 62 1029 1033 1036 1045 -1.6803511
## 63 1026 1034 1038 1042 -1.6750491
## 64 1027 1033 1039 1041 -1.5668099
## 65 1028 1035 1039 1041 -1.5647583
## 66 1028 1032 1039 1041 -1.5639659
## 67 1030 1033 1036 1042 -1.5109156
## 68 1026 1033 1037 1045 -1.5017169
## 69 1029 1033 1040 1041 -1.4493556
## 70 1029 1032 1038 1045 -1.4477843
## 71 1026 1033 1040 1042 -1.4287577
## 72 1027 1034 1038 1045 -1.4224364
## 73 1028 1034 1036 1045 -1.4035177
## 74 1029 1031 1038 1045 -1.4007823
## 75 1028 1031 1037 1045 -1.3837852
## 76 1028 1031 1040 1042 -1.3837003
## 77 1028 1034 1037 1041 -1.3704474
## 78 1029 1035 1037 1043 -1.3447447
## 79 1028 1035 1036 1042 -1.3379690
## 80 1030 1031 1038 1042 -1.3160477
## 81 1027 1035 1039 1043 -1.2746212
## 82 1030 1032 1039 1043 -1.2667283
## 83 1030 1031 1039 1043 -1.2581718
## 84 1027 1031 1039 1043 -1.2407733
## 85 1030 1034 1037 1043 -1.2155303
## 86 1026 1034 1038 1045 -1.2151508
## 87 1026 1035 1038 1042 -1.2088780
## 88 1029 1031 1037 1043 -1.2066846
## 89 1030 1033 1037 1041 -1.2051259
## 90 1028 1034 1040 1041 -1.1992563
## 91 1026 1032 1039 1043 -1.1679179
## 92 1026 1035 1039 1043 -1.1632386
## 93 1027 1033 1036 1045 -1.1346786
## 94 1029 1035 1038 1041 -1.0874779
## 95 1029 1032 1038 1041 -1.0622404
## 96 1026 1034 1037 1043 -1.0577309
## 97 1029 1032 1040 1043 -1.0517986
## 98 1028 1035 1037 1041 -1.0447430
## 99 1029 1032 1036 1043 -1.0353358
## 100 1027 1034 1040 1043 -1.0231825
## 101 1027 1034 1038 1041 -1.0063826
## 102 1030 1034 1038 1041 -0.9975399
## 103 1029 1031 1040 1043 -0.9887564
## 104 1028 1032 1036 1045 -0.9522282
## 105 1027 1031 1038 1045 -0.9286757
## 106 1027 1033 1040 1041 -0.9069473
## 107 1029 1035 1036 1043 -0.8866580
## 108 1026 1034 1040 1043 -0.8337482
## 109 1027 1034 1036 1043 -0.8147813
## 110 1030 1034 1036 1043 -0.7999913
## 111 1030 1031 1037 1043 -0.7969388
## 112 1026 1032 1038 1045 -0.7962529
## 113 1028 1032 1040 1041 -0.7396395
## 114 1026 1035 1037 1043 -0.7119218
## 115 1027 1035 1038 1041 -0.6161209
## 116 1030 1032 1038 1041 -0.5240635
## 117 1027 1031 1040 1043 -0.5222448
## 118 1027 1035 1036 1043 -0.4430857
## 119 1026 1032 1040 1043 -0.4377593
## 120 1030 1032 1036 1043 -0.3648467
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -3.6 0.019 ** moderateClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1030 1031 1037 1044 -5.146101
## 2 1030 1031 1039 1042 -5.072250
## 3 1026 1035 1037 1044 -5.001249
## 4 1026 1035 1039 1042 -4.934501
## 5 1029 1031 1040 1042 -4.847019
## 6 1027 1031 1040 1044 -4.797015
## 7 1029 1035 1036 1042 -4.720641
## 8 1026 1034 1040 1042 -4.640096
## 9 1030 1033 1037 1044 -4.620535
## 10 1029 1031 1037 1045 -4.612677
## 11 1027 1035 1036 1044 -4.598583
## 12 1030 1034 1036 1042 -4.595058
## 13 1027 1031 1039 1045 -4.558706
## 14 1030 1033 1039 1042 -4.509394
## 15 1026 1033 1037 1044 -4.502599
## 16 1026 1032 1040 1044 -4.480598
## 17 1030 1032 1036 1044 -4.458855
## 18 1028 1031 1037 1044 -4.452169
## 19 1028 1035 1037 1044 -4.411982
## 20 1026 1034 1037 1045 -4.391531
## 21 1026 1032 1039 1045 -4.351626
## 22 1026 1033 1039 1042 -4.310219
## 23 1028 1035 1039 1042 -4.298733
## 24 1029 1033 1040 1042 -4.288402
## 25 1028 1031 1039 1042 -4.248685
## 26 1027 1033 1040 1044 -4.236581
## 27 1029 1035 1037 1041 -4.169475
## 28 1029 1033 1037 1045 -4.134178
## 29 1027 1033 1036 1044 -4.121890
## 30 1030 1033 1036 1044 -4.110743
## 31 1029 1033 1036 1042 -4.098189
## 32 1030 1034 1037 1041 -4.060567
## 33 1027 1035 1039 1041 -4.055340
## 34 1029 1032 1036 1045 -4.036830
## 35 1026 1033 1040 1044 -4.026054
## 36 1027 1033 1039 1045 -4.024871
## 37 1028 1032 1040 1044 -4.024487
## 38 1028 1034 1040 1042 -4.012633
## 39 1027 1034 1036 1045 -4.008396
## 40 1028 1032 1036 1044 -3.969436
## 41 1028 1031 1040 1044 -3.957528
## 42 1030 1032 1039 1041 -3.955223
## 43 1029 1035 1038 1042 -3.934064
## 44 1028 1035 1036 1044 -3.917866
## 45 1026 1033 1039 1045 -3.880276
## 46 1029 1031 1038 1042 -3.854964
## 47 1028 1034 1037 1045 -3.854439
## 48 1030 1031 1038 1044 -3.848351
## 49 1028 1034 1036 1042 -3.835532
## 50 1027 1035 1038 1044 -3.818737
## 51 1030 1034 1038 1042 -3.818707
## 52 1029 1032 1040 1041 -3.814186
## 53 1028 1031 1039 1045 -3.810866
## 54 1028 1032 1039 1045 -3.809397
## 55 1027 1031 1038 1044 -3.795204
## 56 1027 1034 1040 1041 -3.785215
## 57 1029 1033 1037 1041 -3.771427
## 58 1026 1032 1038 1044 -3.751469
## 59 1026 1035 1038 1044 -3.734939
## 60 1030 1032 1038 1044 -3.701263
## 61 1027 1033 1039 1041 -3.686460
## 62 1030 1033 1039 1041 -3.663657
## 63 1026 1034 1038 1042 -3.662746
## 64 1029 1033 1036 1045 -3.611549
## 65 1028 1032 1039 1041 -3.550160
## 66 1028 1035 1039 1041 -3.495888
## 67 1030 1033 1036 1042 -3.463478
## 68 1026 1033 1037 1045 -3.456018
## 69 1026 1033 1040 1042 -3.384269
## 70 1029 1033 1040 1041 -3.383492
## 71 1028 1034 1037 1041 -3.356039
## 72 1028 1031 1040 1042 -3.339327
## 73 1028 1031 1037 1045 -3.337990
## 74 1029 1031 1038 1045 -3.334041
## 75 1029 1032 1038 1045 -3.334018
## 76 1028 1034 1036 1045 -3.333319
## 77 1027 1034 1038 1045 -3.308222
## 78 1028 1035 1036 1042 -3.291612
## 79 1030 1031 1038 1042 -3.269202
## 80 1029 1035 1037 1043 -3.235979
## 81 1027 1031 1039 1043 -3.227334
## 82 1029 1031 1037 1043 -3.192817
## 83 1030 1031 1039 1043 -3.176099
## 84 1026 1035 1038 1042 -3.163077
## 85 1027 1035 1039 1043 -3.159892
## 86 1030 1033 1037 1041 -3.157110
## 87 1026 1032 1039 1043 -3.154114
## 88 1026 1034 1038 1045 -3.148024
## 89 1028 1034 1040 1041 -3.131936
## 90 1026 1034 1037 1043 -3.117013
## 91 1030 1034 1037 1043 -3.098275
## 92 1026 1035 1039 1043 -3.094370
## 93 1030 1032 1039 1043 -3.090770
## 94 1027 1033 1036 1045 -3.084860
## 95 1029 1032 1038 1041 -3.048260
## 96 1029 1032 1036 1043 -3.020773
## 97 1029 1035 1038 1041 -3.020002
## 98 1028 1035 1037 1041 -2.997532
## 99 1027 1034 1038 1041 -2.992763
## 100 1029 1032 1040 1043 -2.940788
## 101 1030 1034 1038 1041 -2.927918
## 102 1029 1031 1040 1043 -2.923744
## 103 1027 1034 1040 1043 -2.915505
## 104 1028 1032 1036 1045 -2.901341
## 105 1027 1031 1038 1045 -2.879878
## 106 1027 1033 1040 1041 -2.859200
## 107 1029 1035 1036 1043 -2.817868
## 108 1027 1034 1036 1043 -2.800805
## 109 1026 1034 1040 1043 -2.768333
## 110 1030 1031 1037 1043 -2.748578
## 111 1026 1032 1038 1045 -2.746394
## 112 1030 1034 1036 1043 -2.728791
## 113 1028 1032 1040 1041 -2.690826
## 114 1026 1035 1037 1043 -2.664620
## 115 1027 1035 1038 1041 -2.566863
## 116 1027 1031 1040 1043 -2.473529
## 117 1030 1032 1038 1041 -2.469824
## 118 1027 1035 1036 1043 -2.393025
## 119 1026 1032 1040 1043 -2.389230
## 120 1030 1032 1036 1043 -2.358171MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.2e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.0e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.2e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.0e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.9 0.225 noneClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1058 1062 -0.4481346
## 2 1062 1058 -0.4481346
## 3 1056 1065 -0.4075034
## 4 1065 1056 -0.4075034
## 5 1059 1061 -0.1183263
## 6 1061 1059 -0.1183263
## 7 1057 1062 0.5109625
## 8 1062 1057 0.5109625
## 9 1057 1061 0.5707120
## 10 1061 1057 0.5707120
## 11 1056 1064 0.6454787
## 12 1064 1056 0.6454787
## 13 1059 1060 0.7472458
## 14 1060 1059 0.7472458
## 15 1057 1065 0.7630824
## 16 1065 1057 0.7630824
## 17 1058 1060 0.7757166
## 18 1060 1058 0.7757166
## 19 1056 1063 1.0166883
## 20 1063 1056 1.0166883
## 21 1058 1064 1.1140341
## 22 1064 1058 1.1140341
## 23 1059 1063 1.4921890
## 24 1063 1059 1.4921890
## 25 1060 1065 1.9526951
## 26 1065 1060 1.9526951
## 27 1061 1064 2.0178706
## 28 1064 1061 2.0178706
## 29 1062 1063 2.2088481
## 30 1063 1062 2.2088481
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.6 0.115 noneClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1058 1062 -1.59065258
## 2 1062 1058 -1.59065258
## 3 1057 1062 -1.42882696
## 4 1062 1057 -1.42882696
## 5 1056 1064 -1.28926810
## 6 1064 1056 -1.28926810
## 7 1056 1065 -1.28719394
## 8 1065 1056 -1.28719394
## 9 1059 1061 -1.28604826
## 10 1061 1059 -1.28604826
## 11 1059 1060 -1.20038948
## 12 1060 1059 -1.20038948
## 13 1057 1065 -0.73659724
## 14 1065 1057 -0.73659724
## 15 1058 1064 -0.62129435
## 16 1064 1058 -0.62129435
## 17 1057 1061 -0.25418908
## 18 1061 1057 -0.25418908
## 19 1059 1063 -0.16044582
## 20 1063 1059 -0.16044582
## 21 1058 1060 -0.11351080
## 22 1060 1058 -0.11351080
## 23 1060 1065 0.01814328
## 24 1065 1060 0.01814328
## 25 1061 1064 0.08004895
## 26 1064 1061 0.08004895
## 27 1056 1063 0.19667134
## 28 1063 1056 0.19667134
## 29 1062 1063 0.26649537
## 30 1063 1062 0.26649537Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.
Beta (Bray-Curtis)
response_variable = "bray_curtis"metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Small-Large meta-ecosystem",
"Small-Large unconnected")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)
SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
"Small-Large unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.7e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00397541 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.0e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.6e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00280091 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.2e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.7e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00259059 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -3.9e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.1e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.9e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -2.2e-01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.1e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.7e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.4e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0111113 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -6.9e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+01## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00233093 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -7.2e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -5.9e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -3.3 0.027 ** moderateClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1027 1033 1040 1044 -5.131031
## 2 1027 1034 1040 1043 -4.977195
## 3 1027 1034 1040 1041 -4.905636
## 4 1027 1031 1040 1044 -4.812797
## 5 1027 1033 1040 1041 -4.717979
## 6 1027 1034 1038 1041 -4.715167
## 7 1027 1034 1036 1045 -4.670136
## 8 1027 1035 1036 1044 -4.662253
## 9 1027 1033 1036 1044 -4.637807
## 10 1027 1034 1036 1043 -4.554477
## 11 1027 1031 1040 1043 -4.474211
## 12 1027 1033 1036 1045 -4.436319
## 13 1027 1033 1039 1045 -4.344398
## 14 1027 1035 1036 1043 -4.315984
## 15 1027 1035 1039 1043 -4.204646
## 16 1027 1035 1039 1041 -4.145796
## 17 1029 1032 1040 1043 -4.133475
## 18 1027 1033 1039 1041 -4.119206
## 19 1029 1032 1040 1041 -4.099971
## 20 1027 1031 1039 1045 -4.065356
## 21 1030 1032 1036 1044 -4.000025
## 22 1029 1033 1040 1041 -3.923811
## 23 1027 1031 1039 1043 -3.877826
## 24 1027 1035 1038 1044 -3.850639
## 25 1029 1032 1036 1045 -3.837177
## 26 1027 1034 1038 1045 -3.836793
## 27 1030 1033 1036 1044 -3.794418
## 28 1029 1031 1040 1043 -3.701014
## 29 1030 1032 1036 1043 -3.683937
## 30 1029 1032 1036 1043 -3.683740
## 31 1028 1032 1040 1044 -3.674511
## 32 1026 1032 1040 1044 -3.632629
## 33 1030 1034 1036 1043 -3.631710
## 34 1030 1032 1039 1043 -3.628881
## 35 1030 1032 1039 1041 -3.617396
## 36 1029 1033 1036 1045 -3.600168
## 37 1026 1033 1040 1044 -3.551073
## 38 1027 1031 1038 1044 -3.539664
## 39 1029 1033 1040 1042 -3.533412
## 40 1027 1035 1038 1041 -3.502220
## 41 1030 1033 1039 1041 -3.479676
## 42 1027 1031 1038 1045 -3.456072
## 43 1029 1035 1036 1043 -3.452945
## 44 1028 1031 1040 1044 -3.447980
## 45 1028 1032 1040 1041 -3.429058
## 46 1028 1034 1040 1041 -3.411945
## 47 1029 1031 1040 1042 -3.403523
## 48 1030 1033 1037 1044 -3.385498
## 49 1026 1032 1040 1043 -3.358420
## 50 1026 1034 1040 1043 -3.345094
## 51 1030 1032 1038 1044 -3.325410
## 52 1030 1031 1037 1044 -3.313350
## 53 1030 1031 1039 1043 -3.283020
## 54 1030 1034 1036 1042 -3.209263
## 55 1030 1034 1037 1041 -3.195463
## 56 1030 1033 1037 1041 -3.186302
## 57 1030 1033 1039 1042 -3.160470
## 58 1030 1033 1036 1042 -3.159552
## 59 1030 1034 1037 1043 -3.155227
## 60 1029 1032 1038 1045 -3.154626
## 61 1029 1033 1037 1045 -3.153191
## 62 1028 1034 1040 1042 -3.143799
## 63 1028 1031 1040 1042 -3.140252
## 64 1026 1033 1040 1042 -3.138249
## 65 1028 1032 1036 1044 -3.137845
## 66 1028 1032 1036 1045 -3.104180
## 67 1026 1034 1040 1042 -3.104065
## 68 1030 1031 1037 1043 -3.085122
## 69 1028 1035 1036 1044 -3.082182
## 70 1028 1032 1039 1045 -3.079951
## 71 1029 1031 1037 1045 -3.079872
## 72 1028 1034 1036 1045 -3.071368
## 73 1030 1031 1038 1044 -3.071277
## 74 1030 1031 1039 1042 -3.066697
## 75 1030 1032 1038 1041 -3.054198
## 76 1026 1032 1039 1045 -3.042656
## 77 1030 1034 1038 1041 -3.017531
## 78 1029 1035 1036 1042 -3.005537
## 79 1029 1035 1037 1041 -2.997568
## 80 1026 1033 1039 1045 -2.978107
## 81 1029 1033 1036 1042 -2.977804
## 82 1029 1035 1037 1043 -2.972028
## 83 1029 1032 1038 1041 -2.943027
## 84 1029 1033 1037 1041 -2.938318
## 85 1028 1031 1039 1045 -2.903679
## 86 1029 1031 1038 1045 -2.859475
## 87 1028 1035 1039 1041 -2.856092
## 88 1028 1032 1039 1041 -2.854888
## 89 1028 1031 1037 1045 -2.854281
## 90 1029 1035 1038 1041 -2.838835
## 91 1029 1031 1037 1043 -2.828815
## 92 1028 1035 1037 1044 -2.819852
## 93 1026 1032 1039 1043 -2.806642
## 94 1026 1033 1037 1045 -2.804241
## 95 1028 1034 1037 1045 -2.795984
## 96 1026 1035 1039 1043 -2.785781
## 97 1026 1035 1037 1044 -2.780723
## 98 1026 1034 1037 1045 -2.754030
## 99 1028 1031 1037 1044 -2.727819
## 100 1030 1034 1038 1042 -2.713690
## 101 1026 1033 1037 1044 -2.711566
## 102 1028 1035 1037 1041 -2.699511
## 103 1030 1031 1038 1042 -2.677046
## 104 1028 1035 1039 1042 -2.634773
## 105 1028 1035 1036 1042 -2.620015
## 106 1026 1035 1039 1042 -2.598459
## 107 1028 1034 1037 1041 -2.577819
## 108 1026 1035 1037 1043 -2.575947
## 109 1028 1034 1036 1042 -2.568613
## 110 1026 1032 1038 1045 -2.565685
## 111 1026 1035 1038 1044 -2.556292
## 112 1026 1032 1038 1044 -2.551427
## 113 1028 1031 1039 1042 -2.549840
## 114 1026 1033 1039 1042 -2.545385
## 115 1026 1034 1038 1045 -2.536037
## 116 1029 1035 1038 1042 -2.516755
## 117 1026 1034 1037 1043 -2.480185
## 118 1029 1031 1038 1042 -2.399991
## 119 1026 1035 1038 1042 -2.226465
## 120 1026 1034 1038 1042 -2.125076
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -4.6 0.012 ** moderateClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1027 1033 1040 1044 -6.940532
## 2 1027 1034 1040 1043 -6.903324
## 3 1027 1034 1040 1041 -6.760521
## 4 1027 1034 1038 1041 -6.622166
## 5 1027 1034 1036 1045 -6.606294
## 6 1027 1033 1036 1044 -6.577876
## 7 1027 1035 1036 1044 -6.562129
## 8 1027 1034 1036 1043 -6.549768
## 9 1027 1031 1040 1044 -6.452391
## 10 1027 1033 1040 1041 -6.371757
## 11 1027 1033 1036 1045 -6.220793
## 12 1027 1035 1036 1043 -6.186646
## 13 1027 1033 1039 1045 -6.096878
## 14 1027 1031 1040 1043 -6.057354
## 15 1027 1035 1039 1043 -6.049751
## 16 1029 1032 1040 1043 -5.933082
## 17 1027 1033 1039 1041 -5.930748
## 18 1027 1035 1039 1041 -5.897280
## 19 1029 1032 1040 1041 -5.794994
## 20 1030 1032 1036 1044 -5.757495
## 21 1027 1034 1038 1045 -5.697180
## 22 1027 1035 1038 1044 -5.662918
## 23 1029 1032 1036 1045 -5.651213
## 24 1027 1031 1039 1045 -5.633029
## 25 1027 1031 1039 1043 -5.629971
## 26 1029 1032 1036 1043 -5.617087
## 27 1030 1032 1036 1043 -5.394408
## 28 1030 1032 1039 1043 -5.306848
## 29 1029 1033 1040 1041 -5.292856
## 30 1030 1034 1036 1043 -5.287809
## 31 1027 1031 1038 1044 -5.254627
## 32 1030 1033 1036 1044 -5.254242
## 33 1030 1032 1039 1041 -5.168969
## 34 1028 1032 1040 1044 -5.158396
## 35 1027 1035 1038 1041 -5.156805
## 36 1026 1032 1040 1044 -5.142217
## 37 1029 1033 1036 1045 -5.138453
## 38 1029 1035 1036 1043 -5.113887
## 39 1029 1031 1040 1043 -4.984868
## 40 1030 1032 1038 1044 -4.955229
## 41 1027 1031 1038 1045 -4.902859
## 42 1029 1032 1038 1045 -4.853952
## 43 1028 1032 1036 1044 -4.840536
## 44 1026 1032 1040 1043 -4.801060
## 45 1026 1034 1040 1043 -4.726029
## 46 1026 1033 1040 1044 -4.691634
## 47 1028 1032 1040 1041 -4.676531
## 48 1030 1033 1039 1041 -4.663205
## 49 1029 1032 1038 1041 -4.619450
## 50 1028 1034 1040 1041 -4.596171
## 51 1028 1032 1036 1045 -4.535937
## 52 1029 1033 1040 1042 -4.504157
## 53 1028 1032 1039 1045 -4.479165
## 54 1030 1032 1038 1041 -4.472011
## 55 1026 1032 1039 1045 -4.470568
## 56 1026 1032 1039 1043 -4.444710
## 57 1028 1034 1036 1045 -4.442180
## 58 1028 1035 1036 1044 -4.379247
## 59 1030 1031 1039 1043 -4.376579
## 60 1030 1034 1036 1042 -4.375624
## 61 1030 1034 1038 1041 -4.374437
## 62 1030 1034 1037 1043 -4.364962
## 63 1028 1032 1039 1041 -4.338405
## 64 1030 1033 1037 1044 -4.327466
## 65 1028 1031 1040 1044 -4.267812
## 66 1029 1033 1036 1042 -4.263918
## 67 1030 1034 1037 1041 -4.212466
## 68 1029 1033 1037 1045 -4.209670
## 69 1029 1035 1038 1041 -4.208528
## 70 1029 1035 1037 1043 -4.198452
## 71 1029 1035 1036 1042 -4.186153
## 72 1026 1032 1038 1044 -4.139370
## 73 1029 1033 1037 1041 -4.099395
## 74 1030 1031 1038 1044 -4.095837
## 75 1029 1031 1040 1042 -4.063453
## 76 1029 1035 1037 1041 -4.035656
## 77 1026 1033 1039 1045 -4.016902
## 78 1026 1035 1039 1043 -3.994497
## 79 1029 1031 1038 1045 -3.981474
## 80 1030 1031 1037 1044 -3.955214
## 81 1030 1033 1036 1042 -3.932411
## 82 1030 1033 1039 1042 -3.903767
## 83 1026 1034 1040 1042 -3.899653
## 84 1029 1031 1037 1043 -3.897016
## 85 1028 1034 1040 1042 -3.887318
## 86 1028 1035 1039 1041 -3.849173
## 87 1026 1032 1038 1045 -3.846206
## 88 1029 1031 1037 1045 -3.834051
## 89 1030 1033 1037 1041 -3.795195
## 90 1026 1034 1038 1045 -3.755427
## 91 1026 1035 1038 1044 -3.696892
## 92 1030 1034 1038 1042 -3.656193
## 93 1028 1034 1036 1042 -3.649720
## 94 1026 1034 1037 1043 -3.646837
## 95 1026 1034 1037 1045 -3.620843
## 96 1026 1033 1037 1044 -3.612827
## 97 1028 1034 1037 1045 -3.610219
## 98 1028 1031 1039 1045 -3.606477
## 99 1030 1031 1037 1043 -3.599894
## 100 1026 1035 1037 1044 -3.563164
## 101 1028 1035 1037 1044 -3.549454
## 102 1028 1034 1037 1041 -3.503951
## 103 1029 1035 1038 1042 -3.482353
## 104 1026 1033 1040 1042 -3.482214
## 105 1030 1031 1039 1042 -3.478937
## 106 1028 1031 1037 1044 -3.273757
## 107 1026 1033 1039 1042 -3.244087
## 108 1026 1033 1037 1045 -3.243225
## 109 1026 1035 1037 1043 -3.240657
## 110 1029 1031 1038 1042 -3.184571
## 111 1026 1035 1039 1042 -3.170945
## 112 1028 1035 1036 1042 -3.165473
## 113 1028 1035 1039 1042 -3.153646
## 114 1028 1035 1037 1041 -3.060612
## 115 1028 1031 1040 1042 -3.048588
## 116 1026 1034 1038 1042 -3.025000
## 117 1028 1031 1037 1045 -2.878668
## 118 1028 1031 1039 1042 -2.857615
## 119 1030 1031 1038 1042 -2.833675
## 120 1026 1035 1038 1042 -2.557163MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222507 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222133 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.2e+02## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222507 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00222133 (tol = 0.002, component 1)## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -4.2e+02## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning: Model failed to converge with 1 negative eigenvalue: -1.8e+00## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2.1 0.469 noneClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1059 1061 -2.1634950
## 2 1061 1059 -2.1634950
## 3 1061 1064 0.3104198
## 4 1064 1061 0.3104198
## 5 1058 1062 0.6299275
## 6 1062 1058 0.6299275
## 7 1058 1064 1.4703315
## 8 1064 1058 1.4703315
## 9 1059 1060 1.8363618
## 10 1060 1059 1.8363618
## 11 1056 1065 2.3113527
## 12 1065 1056 2.3113527
## 13 1056 1064 2.4258678
## 14 1064 1056 2.4258678
## 15 1057 1062 2.8145259
## 16 1062 1057 2.8145259
## 17 1059 1063 2.9451644
## 18 1063 1059 2.9451644
## 19 1058 1060 2.9492200
## 20 1060 1058 2.9492200
## 21 1057 1061 2.9921157
## 22 1061 1057 2.9921157
## 23 1062 1063 3.0082645
## 24 1063 1062 3.0082645
## 25 1060 1065 3.1739693
## 26 1065 1060 3.1739693
## 27 1056 1063 3.3683048
## 28 1063 1056 3.3683048
## 29 1057 1065 3.5740379
## 30 1065 1057 3.5740379
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.7 0.333 noneClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1059 1061 -1.8677401
## 2 1061 1059 -1.8677401
## 3 1058 1062 -1.3609533
## 4 1062 1058 -1.3609533
## 5 1061 1064 0.3699422
## 6 1064 1061 0.3699422
## 7 1058 1064 0.6864549
## 8 1064 1058 0.6864549
## 9 1059 1060 0.7170381
## 10 1060 1059 0.7170381
## 11 1056 1065 0.8343727
## 12 1065 1056 0.8343727
## 13 1058 1060 0.9528356
## 14 1060 1058 0.9528356
## 15 1057 1062 0.9795774
## 16 1062 1057 0.9795774
## 17 1057 1061 0.9976548
## 18 1061 1057 0.9976548
## 19 1056 1064 1.1258105
## 20 1064 1056 1.1258105
## 21 1059 1063 1.2673148
## 22 1063 1059 1.2673148
## 23 1062 1063 1.2753382
## 24 1063 1062 1.2753382
## 25 1056 1063 1.5564216
## 26 1063 1056 1.5564216
## 27 1060 1065 1.7486191
## 28 1065 1060 1.7486191
## 29 1057 1065 1.8526093
## 30 1065 1057 1.8526093Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.
Gamma (regional richness)
response_variable = "metaecosystem_richness"metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Small-Large meta-ecosystem",
"Small-Large unconnected")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)
SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
"Small-Large unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2.2 0.449 noneClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1027 1031 1040 1043 0.1184054
## 2 1026 1032 1040 1043 0.4857987
## 3 1030 1032 1036 1043 0.5916539
## 4 1027 1035 1036 1043 0.5916539
## 5 1027 1033 1036 1045 0.6185128
## 6 1027 1033 1040 1041 0.6262096
## 7 1026 1035 1037 1043 0.8013854
## 8 1027 1031 1038 1045 0.8028149
## 9 1030 1031 1037 1043 0.8234183
## 10 1028 1032 1036 1045 0.8765712
## 11 1028 1032 1040 1041 0.9116171
## 12 1026 1033 1037 1045 0.9247340
## 13 1028 1031 1037 1045 0.9435650
## 14 1026 1032 1038 1045 0.9707246
## 15 1028 1031 1040 1042 1.0032662
## 16 1026 1033 1040 1042 1.0124658
## 17 1026 1035 1038 1042 1.0483023
## 18 1028 1035 1037 1041 1.0531285
## 19 1027 1035 1038 1041 1.1313847
## 20 1030 1032 1038 1041 1.1313847
## 21 1030 1031 1038 1042 1.1415923
## 22 1030 1033 1037 1041 1.1415923
## 23 1028 1035 1036 1042 1.1817598
## 24 1030 1033 1036 1042 1.2068920
## 25 1029 1031 1040 1043 1.4738514
## 26 1026 1033 1040 1044 1.6449245
## 27 1028 1031 1040 1044 1.6888776
## 28 1029 1033 1036 1045 1.6953488
## 29 1029 1035 1036 1043 1.6965544
## 30 1026 1035 1038 1044 1.7039081
## 31 1029 1033 1040 1041 1.7112135
## 32 1029 1031 1038 1045 1.7171764
## 33 1030 1033 1036 1044 1.7401448
## 34 1030 1031 1038 1044 1.7500094
## 35 1027 1033 1036 1044 1.7719847
## 36 1029 1032 1036 1043 1.8089431
## 37 1029 1035 1038 1041 1.8187599
## 38 1028 1035 1036 1044 1.8392635
## 39 1027 1031 1039 1043 1.8578998
## 40 1026 1034 1038 1045 1.9171187
## 41 1030 1031 1039 1043 1.9248196
## 42 1026 1034 1040 1043 1.9751176
## 43 1026 1035 1039 1043 2.0164777
## 44 1027 1031 1038 1044 2.0304657
## 45 1026 1033 1039 1045 2.0546512
## 46 1028 1032 1036 1044 2.0694046
## 47 1030 1034 1038 1041 2.0694600
## 48 1030 1034 1036 1043 2.0904245
## 49 1028 1031 1039 1045 2.0907961
## 50 1028 1034 1036 1045 2.1082731
## 51 1030 1033 1039 1041 2.1379006
## 52 1028 1034 1040 1041 2.1437119
## 53 1029 1031 1037 1043 2.1498037
## 54 1027 1033 1040 1044 2.1523181
## 55 1026 1032 1039 1043 2.1720464
## 56 1029 1032 1040 1043 2.1774126
## 57 1027 1033 1039 1041 2.1984253
## 58 1026 1033 1037 1044 2.2119163
## 59 1026 1032 1038 1044 2.2222913
## 60 1028 1035 1039 1041 2.2389915
## 61 1029 1033 1036 1042 2.2627048
## 62 1027 1034 1036 1043 2.2640377
## 63 1029 1032 1038 1041 2.2653341
## 64 1028 1031 1037 1044 2.2727205
## 65 1029 1031 1038 1042 2.2920731
## 66 1029 1033 1037 1041 2.2920731
## 67 1026 1034 1037 1043 2.4002606
## 68 1026 1034 1038 1042 2.4401378
## 69 1028 1032 1039 1041 2.4419863
## 70 1028 1032 1040 1044 2.4485679
## 71 1028 1034 1037 1041 2.5024721
## 72 1027 1033 1039 1045 2.5293857
## 73 1026 1033 1039 1042 2.5511370
## 74 1027 1035 1039 1043 2.5643376
## 75 1030 1032 1039 1043 2.5643376
## 76 1028 1031 1039 1042 2.5780819
## 77 1027 1034 1038 1041 2.5811953
## 78 1027 1034 1040 1043 2.5913595
## 79 1028 1034 1036 1042 2.6035722
## 80 1029 1032 1038 1045 2.6456581
## 81 1029 1033 1040 1042 2.6577686
## 82 1029 1035 1037 1043 2.6591291
## 83 1030 1032 1038 1044 2.6712469
## 84 1027 1035 1038 1044 2.6712469
## 85 1029 1033 1037 1045 2.6896263
## 86 1030 1033 1037 1044 2.7148934
## 87 1028 1035 1037 1044 2.7328657
## 88 1029 1035 1038 1042 2.7658189
## 89 1028 1032 1039 1045 2.7744574
## 90 1028 1034 1037 1045 2.8568194
## 91 1030 1034 1037 1043 2.8772512
## 92 1030 1034 1038 1042 2.9228228
## 93 1027 1034 1038 1045 2.9266862
## 94 1030 1033 1039 1042 2.9600778
## 95 1028 1034 1040 1042 2.9759999
## 96 1028 1035 1039 1042 3.0345699
## 97 1027 1031 1040 1044 3.0487703
## 98 1026 1034 1037 1045 3.2227518
## 99 1026 1035 1037 1044 3.2254653
## 100 1026 1032 1040 1044 3.2793631
## 101 1029 1032 1040 1041 3.3026595
## 102 1029 1032 1036 1045 3.3026595
## 103 1027 1031 1039 1045 3.3100834
## 104 1027 1035 1036 1044 3.3277203
## 105 1030 1032 1036 1044 3.3277203
## 106 1029 1035 1037 1041 3.3536689
## 107 1029 1031 1037 1045 3.3754843
## 108 1030 1034 1037 1041 3.3859468
## 109 1030 1031 1037 1044 3.3985584
## 110 1029 1031 1040 1042 3.4247298
## 111 1026 1032 1039 1045 3.4830031
## 112 1026 1034 1040 1042 3.4877050
## 113 1029 1035 1036 1042 3.5066722
## 114 1026 1035 1039 1042 3.5081735
## 115 1027 1034 1036 1045 3.5265898
## 116 1030 1032 1039 1041 3.5265898
## 117 1027 1035 1039 1041 3.5265898
## 118 1027 1034 1040 1041 3.5265898
## 119 1030 1031 1039 1042 3.5793863
## 120 1030 1034 1036 1042 3.5994587
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.7 0.318 noneClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1027 1031 1040 1043 -1.65718236
## 2 1027 1033 1036 1045 -1.12259736
## 3 1027 1033 1040 1041 -1.11490052
## 4 1030 1032 1036 1043 -1.05919932
## 5 1027 1035 1036 1043 -1.05919932
## 6 1026 1032 1040 1043 -1.04956469
## 7 1027 1031 1038 1045 -0.66691460
## 8 1028 1032 1036 1045 -0.60753760
## 9 1028 1032 1040 1041 -0.59117420
## 10 1027 1033 1036 1044 -0.16441858
## 11 1027 1035 1038 1041 -0.16035273
## 12 1030 1032 1038 1041 -0.16035273
## 13 1026 1032 1038 1045 -0.15068719
## 14 1030 1031 1037 1043 -0.13808816
## 15 1026 1033 1040 1042 -0.13712296
## 16 1028 1031 1040 1042 -0.12343883
## 17 1030 1033 1036 1042 -0.10750634
## 18 1027 1031 1039 1043 -0.08266643
## 19 1029 1032 1036 1043 -0.07728127
## 20 1029 1031 1040 1043 -0.05377605
## 21 1027 1033 1040 1044 0.16866674
## 22 1029 1033 1036 1045 0.21963355
## 23 1029 1032 1040 1043 0.22264762
## 24 1029 1033 1040 1041 0.23549825
## 25 1030 1031 1038 1042 0.24054564
## 26 1030 1033 1037 1041 0.24054564
## 27 1026 1033 1037 1045 0.24074956
## 28 1027 1031 1038 1044 0.24477102
## 29 1030 1033 1036 1044 0.24725672
## 30 1028 1032 1036 1044 0.26982886
## 31 1027 1033 1039 1041 0.27946580
## 32 1028 1035 1036 1042 0.28071311
## 33 1026 1033 1040 1044 0.28834590
## 34 1028 1031 1037 1045 0.29106203
## 35 1028 1031 1040 1044 0.30541988
## 36 1026 1035 1037 1043 0.30952771
## 37 1029 1035 1036 1043 0.34596173
## 38 1026 1032 1039 1043 0.36299333
## 39 1027 1034 1036 1043 0.40380312
## 40 1030 1031 1039 1043 0.41788013
## 41 1028 1032 1040 1044 0.55483412
## 42 1027 1033 1039 1045 0.55688420
## 43 1029 1033 1036 1042 0.60427912
## 44 1029 1032 1038 1041 0.61624107
## 45 1029 1031 1038 1045 0.61937207
## 46 1030 1031 1038 1044 0.62186766
## 47 1027 1035 1039 1043 0.62481978
## 48 1030 1032 1039 1043 0.62481978
## 49 1026 1035 1038 1042 0.62533298
## 50 1027 1034 1040 1043 0.65487306
## 51 1026 1032 1038 1044 0.65551858
## 52 1028 1032 1039 1041 0.65964771
## 53 1028 1035 1037 1041 0.67724089
## 54 1028 1035 1036 1044 0.68283289
## 55 1030 1033 1039 1041 0.69260830
## 56 1026 1033 1039 1045 0.71993955
## 57 1028 1031 1039 1045 0.72958735
## 58 1029 1031 1037 1043 0.73056357
## 59 1030 1034 1036 1043 0.78930670
## 60 1026 1035 1039 1043 0.81408505
## 61 1026 1034 1040 1043 0.82276296
## 62 1029 1032 1038 1045 0.86936025
## 63 1029 1033 1040 1042 0.87467163
## 64 1030 1032 1038 1044 0.88814996
## 65 1027 1035 1038 1044 0.88814996
## 66 1028 1032 1039 1045 0.90080080
## 67 1029 1031 1038 1042 0.93786621
## 68 1029 1033 1037 1041 0.93786621
## 69 1029 1035 1038 1041 0.94861787
## 70 1027 1034 1038 1041 0.97315483
## 71 1026 1033 1037 1044 0.98256355
## 72 1026 1035 1038 1044 1.00185638
## 73 1028 1031 1037 1044 1.01488846
## 74 1026 1033 1039 1042 1.01902222
## 75 1028 1031 1039 1042 1.02881099
## 76 1028 1034 1036 1045 1.03825704
## 77 1027 1031 1040 1044 1.04877028
## 78 1028 1034 1040 1041 1.05277914
## 79 1028 1035 1039 1041 1.07471304
## 80 1029 1033 1037 1045 1.16109065
## 81 1030 1033 1037 1044 1.17068843
## 82 1027 1034 1038 1045 1.18601448
## 83 1030 1033 1039 1042 1.20764640
## 84 1029 1035 1037 1043 1.24335157
## 85 1030 1034 1038 1041 1.26608050
## 86 1028 1034 1036 1042 1.28287675
## 87 1027 1031 1039 1045 1.31211837
## 88 1026 1034 1038 1045 1.31901954
## 89 1029 1032 1040 1041 1.32074576
## 90 1029 1032 1036 1045 1.32074576
## 91 1026 1032 1040 1044 1.32900261
## 92 1027 1035 1036 1044 1.34515254
## 93 1030 1032 1036 1044 1.34515254
## 94 1026 1034 1037 1043 1.38664507
## 95 1029 1035 1038 1042 1.41161197
## 96 1028 1034 1040 1042 1.47078486
## 97 1028 1035 1037 1044 1.48160821
## 98 1028 1035 1039 1042 1.49063338
## 99 1030 1034 1037 1043 1.51063165
## 100 1026 1034 1038 1042 1.51519213
## 101 1026 1032 1039 1045 1.55016501
## 102 1029 1031 1040 1042 1.55227262
## 103 1028 1034 1037 1041 1.55503012
## 104 1027 1034 1036 1045 1.55803538
## 105 1030 1032 1039 1041 1.55803538
## 106 1027 1035 1039 1041 1.55803538
## 107 1027 1034 1040 1041 1.55803538
## 108 1030 1034 1038 1042 1.62528090
## 109 1028 1034 1037 1045 1.69248914
## 110 1029 1031 1037 1045 1.72370911
## 111 1030 1031 1037 1044 1.73388560
## 112 1030 1031 1039 1042 1.73759816
## 113 1029 1035 1036 1042 1.74052995
## 114 1029 1035 1037 1041 1.86624986
## 115 1026 1035 1037 1044 1.86807498
## 116 1026 1034 1040 1042 1.86966260
## 117 1030 1034 1036 1042 1.87287701
## 118 1026 1035 1039 1042 1.87634137
## 119 1026 1034 1037 1045 1.95401191
## 120 1030 1034 1037 1041 1.95521289MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
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Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2.8 0.576 noneClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1057 1062 1.295857
## 2 1062 1057 1.295857
## 3 1059 1060 1.891039
## 4 1060 1059 1.891039
## 5 1058 1062 2.005519
## 6 1062 1058 2.005519
## 7 1056 1064 2.007075
## 8 1064 1056 2.007075
## 9 1062 1063 2.635024
## 10 1063 1062 2.635024
## 11 1058 1064 2.758295
## 12 1064 1058 2.758295
## 13 1060 1065 2.918645
## 14 1065 1060 2.918645
## 15 1059 1061 3.032444
## 16 1059 1063 3.032444
## 17 1061 1059 3.032444
## 18 1063 1059 3.032444
## 19 1057 1065 3.102242
## 20 1065 1057 3.102242
## 21 1058 1060 3.125725
## 22 1060 1058 3.125725
## 23 1056 1065 3.199072
## 24 1065 1056 3.199072
## 25 1061 1064 3.286048
## 26 1064 1061 3.286048
## 27 1057 1061 3.772903
## 28 1061 1057 3.772903
## 29 1056 1063 3.782587
## 30 1063 1056 3.782587
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.5 0.62 noneClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1058 1062 0.02558494
## 2 1062 1058 0.02558494
## 3 1058 1064 0.76954896
## 4 1064 1058 0.76954896
## 5 1059 1060 1.13564061
## 6 1060 1059 1.13564061
## 7 1059 1061 1.14448056
## 8 1059 1063 1.14448056
## 9 1061 1059 1.14448056
## 10 1063 1059 1.14448056
## 11 1058 1060 1.20081237
## 12 1060 1058 1.20081237
## 13 1062 1063 1.61235729
## 14 1063 1062 1.61235729
## 15 1057 1062 1.79492711
## 16 1062 1057 1.79492711
## 17 1057 1065 1.92328025
## 18 1065 1057 1.92328025
## 19 1061 1064 1.94501477
## 20 1064 1061 1.94501477
## 21 1056 1065 1.96756892
## 22 1065 1056 1.96756892
## 23 1056 1064 1.99173842
## 24 1064 1056 1.99173842
## 25 1056 1063 1.99458722
## 26 1063 1056 1.99458722
## 27 1060 1065 1.99783118
## 28 1065 1060 1.99783118
## 29 1057 1061 1.99859706
## 30 1061 1057 1.99859706Biomass
response_variable = "total_metaecosystem_bioarea_mm2"metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Small-Large meta-ecosystem",
"Small-Large unconnected")Here we want to look at how this meta-ecosystem variable changed across time by plotting its mean ± 95 confidence interval:
plot.metaecos.points(ds_metaecosystems,
metaecosystem_type_i,
response_variable,
3)
Click here to view the same data represented through the single replicates
plot.metaecos.replicates(ds_metaecosystems,
metaecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among meta-ecosystems. To make it easier to interpret differences, we decided to construct a model for each comparisons we are interested in, which are: asymmetric vs symmetric connected, asymmetric connected vs unconnected, and symmetric connected vs unconnected.
SL (connected vs unconnected)
metaecosystem_type_i = c("Small-Large meta-ecosystem",
"Small-Large unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -5.1 0.011 ** moderateClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1029 1035 1038 1042 -6.022025
## 2 1028 1035 1039 1042 -6.009392
## 3 1029 1032 1038 1045 -5.980998
## 4 1028 1035 1036 1042 -5.971627
## 5 1028 1032 1039 1045 -5.968418
## 6 1029 1035 1037 1043 -5.964009
## 7 1030 1032 1039 1043 -5.953994
## 8 1030 1033 1039 1042 -5.952080
## 9 1027 1035 1039 1043 -5.950406
## 10 1026 1035 1038 1042 -5.949312
## 11 1030 1032 1038 1044 -5.935165
## 12 1030 1034 1038 1042 -5.933681
## 13 1027 1035 1038 1041 -5.932083
## 14 1028 1035 1037 1041 -5.932061
## 15 1027 1035 1036 1043 -5.931435
## 16 1028 1035 1037 1044 -5.931425
## 17 1027 1035 1038 1044 -5.930187
## 18 1028 1032 1036 1045 -5.929937
## 19 1029 1033 1037 1045 -5.922847
## 20 1029 1032 1040 1043 -5.915603
## 21 1029 1033 1040 1042 -5.913018
## 22 1027 1033 1039 1045 -5.911002
## 23 1026 1035 1037 1043 -5.910253
## 24 1026 1032 1038 1045 -5.907733
## 25 1028 1034 1037 1045 -5.891026
## 26 1027 1034 1038 1045 -5.890883
## 27 1027 1033 1036 1045 -5.890744
## 28 1030 1032 1036 1043 -5.885985
## 29 1030 1032 1038 1041 -5.885243
## 30 1028 1032 1040 1044 -5.884380
## 31 1030 1033 1036 1042 -5.882925
## 32 1028 1034 1040 1042 -5.882767
## 33 1030 1033 1037 1044 -5.875438
## 34 1030 1034 1037 1043 -5.875257
## 35 1027 1031 1038 1045 -5.873727
## 36 1028 1031 1037 1045 -5.873315
## 37 1026 1033 1037 1045 -5.870195
## 38 1030 1031 1038 1042 -5.864916
## 39 1028 1032 1040 1041 -5.845141
## 40 1030 1033 1037 1041 -5.842017
## 41 1030 1031 1037 1043 -5.826602
## 42 1027 1033 1040 1044 -5.826177
## 43 1027 1034 1040 1043 -5.825908
## 44 1028 1031 1040 1042 -5.825505
## 45 1026 1032 1040 1043 -5.825061
## 46 1026 1033 1040 1042 -5.823777
## 47 1027 1033 1040 1041 -5.805192
## 48 1027 1031 1040 1043 -5.789613
## 49 1029 1035 1036 1042 -5.251301
## 50 1029 1035 1037 1041 -5.214670
## 51 1029 1032 1036 1045 -5.213476
## 52 1026 1035 1039 1042 -5.206071
## 53 1030 1032 1039 1041 -5.199912
## 54 1027 1035 1039 1041 -5.195244
## 55 1030 1031 1039 1042 -5.186668
## 56 1029 1032 1040 1041 -5.170284
## 57 1030 1034 1036 1042 -5.168899
## 58 1026 1032 1039 1045 -5.168465
## 59 1029 1031 1037 1045 -5.165148
## 60 1030 1032 1036 1044 -5.161803
## 61 1029 1031 1040 1042 -5.156784
## 62 1027 1035 1036 1044 -5.155613
## 63 1027 1031 1039 1045 -5.146903
## 64 1030 1034 1037 1041 -5.131450
## 65 1026 1035 1037 1044 -5.130977
## 66 1027 1034 1036 1045 -5.127348
## 67 1030 1031 1037 1044 -5.112757
## 68 1026 1034 1037 1045 -5.102779
## 69 1026 1034 1040 1042 -5.096091
## 70 1026 1032 1040 1044 -5.088332
## 71 1027 1034 1040 1041 -5.084501
## 72 1027 1031 1040 1044 -5.065938
## 73 1029 1033 1036 1042 -4.434082
## 74 1029 1031 1038 1042 -4.432915
## 75 1029 1032 1038 1041 -4.430208
## 76 1028 1031 1039 1042 -4.415847
## 77 1028 1032 1039 1041 -4.412631
## 78 1029 1032 1036 1043 -4.405513
## 79 1029 1033 1037 1041 -4.405467
## 80 1029 1031 1037 1043 -4.381131
## 81 1028 1034 1036 1042 -4.376436
## 82 1026 1033 1039 1042 -4.374303
## 83 1027 1033 1039 1041 -4.367195
## 84 1028 1032 1036 1044 -4.349511
## 85 1028 1034 1037 1041 -4.348239
## 86 1026 1032 1039 1043 -4.344340
## 87 1027 1031 1039 1043 -4.342572
## 88 1026 1034 1038 1042 -4.333840
## 89 1027 1034 1038 1041 -4.326583
## 90 1028 1031 1037 1044 -4.326530
## 91 1026 1032 1038 1044 -4.306005
## 92 1027 1031 1038 1044 -4.304605
## 93 1027 1033 1036 1044 -4.304519
## 94 1029 1033 1036 1045 -4.304489
## 95 1027 1034 1036 1043 -4.301859
## 96 1029 1035 1038 1041 -4.301289
## 97 1029 1035 1036 1043 -4.296825
## 98 1028 1035 1039 1041 -4.295904
## 99 1029 1031 1038 1045 -4.292952
## 100 1028 1031 1039 1045 -4.287696
## 101 1026 1033 1037 1044 -4.284830
## 102 1026 1034 1037 1043 -4.282201
## 103 1026 1033 1039 1045 -4.273499
## 104 1026 1035 1039 1043 -4.265870
## 105 1028 1035 1036 1044 -4.244515
## 106 1028 1034 1036 1045 -4.241291
## 107 1029 1033 1040 1041 -4.224922
## 108 1030 1033 1039 1041 -4.222213
## 109 1026 1035 1038 1044 -4.218484
## 110 1026 1034 1038 1045 -4.215300
## 111 1029 1031 1040 1043 -4.209660
## 112 1030 1031 1039 1043 -4.206887
## 113 1030 1033 1036 1044 -4.173196
## 114 1030 1034 1038 1041 -4.166109
## 115 1028 1034 1040 1041 -4.163908
## 116 1030 1031 1038 1044 -4.161992
## 117 1030 1034 1036 1043 -4.161909
## 118 1028 1031 1040 1044 -4.159809
## 119 1026 1033 1040 1044 -4.146483
## 120 1026 1034 1040 1043 -4.135442
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -6.9 0.003 *** strongClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1028 1035 1036 1042 -7.963705
## 2 1029 1035 1038 1042 -7.944556
## 3 1026 1035 1038 1042 -7.941393
## 4 1028 1035 1039 1042 -7.932491
## 5 1028 1035 1037 1041 -7.923836
## 6 1027 1035 1038 1041 -7.923739
## 7 1027 1035 1036 1043 -7.923088
## 8 1028 1032 1036 1045 -7.921975
## 9 1029 1032 1038 1045 -7.903120
## 10 1026 1035 1037 1043 -7.902029
## 11 1026 1032 1038 1045 -7.899773
## 12 1028 1032 1039 1045 -7.891113
## 13 1029 1035 1037 1043 -7.883289
## 14 1027 1033 1036 1045 -7.882434
## 15 1030 1032 1036 1043 -7.877800
## 16 1030 1032 1038 1041 -7.877061
## 17 1030 1033 1036 1042 -7.874818
## 18 1030 1032 1039 1043 -7.874419
## 19 1030 1033 1039 1042 -7.873254
## 20 1027 1035 1039 1043 -7.869099
## 21 1027 1031 1038 1045 -7.865420
## 22 1028 1031 1037 1045 -7.865127
## 23 1026 1033 1037 1045 -7.862007
## 24 1030 1032 1038 1044 -7.857041
## 25 1030 1031 1038 1042 -7.856812
## 26 1030 1034 1038 1042 -7.855904
## 27 1028 1035 1037 1044 -7.852789
## 28 1027 1035 1038 1044 -7.850394
## 29 1029 1033 1037 1045 -7.842469
## 30 1028 1032 1040 1041 -7.837021
## 31 1029 1032 1040 1043 -7.836058
## 32 1029 1033 1040 1042 -7.834225
## 33 1030 1033 1037 1041 -7.833593
## 34 1027 1033 1039 1045 -7.830037
## 35 1030 1031 1037 1043 -7.818179
## 36 1028 1031 1040 1042 -7.817462
## 37 1026 1032 1040 1043 -7.816942
## 38 1026 1033 1040 1042 -7.815735
## 39 1028 1034 1037 1045 -7.812332
## 40 1027 1034 1038 1045 -7.811026
## 41 1028 1032 1040 1044 -7.806862
## 42 1028 1034 1040 1042 -7.805594
## 43 1027 1033 1040 1041 -7.796711
## 44 1030 1033 1037 1044 -7.794803
## 45 1030 1034 1037 1043 -7.794217
## 46 1027 1031 1040 1043 -7.781132
## 47 1027 1033 1040 1044 -7.744992
## 48 1027 1034 1040 1043 -7.744316
## 49 1029 1035 1036 1042 -7.152003
## 50 1029 1032 1036 1045 -7.113658
## 51 1029 1035 1037 1041 -7.111188
## 52 1026 1035 1039 1042 -7.107568
## 53 1030 1032 1039 1041 -7.097960
## 54 1027 1035 1039 1041 -7.091016
## 55 1030 1031 1039 1042 -7.085682
## 56 1026 1032 1039 1045 -7.069452
## 57 1030 1034 1036 1042 -7.069254
## 58 1029 1032 1040 1041 -7.068363
## 59 1029 1031 1037 1045 -7.062114
## 60 1030 1032 1036 1044 -7.061722
## 61 1029 1031 1040 1042 -7.055832
## 62 1027 1035 1036 1044 -7.053333
## 63 1027 1031 1039 1045 -7.043125
## 64 1026 1035 1037 1044 -7.030250
## 65 1030 1034 1037 1041 -7.027609
## 66 1027 1034 1036 1045 -7.024986
## 67 1030 1031 1037 1044 -7.009450
## 68 1026 1034 1037 1045 -7.001977
## 69 1026 1034 1040 1042 -6.997288
## 70 1026 1032 1040 1044 -6.989097
## 71 1027 1034 1040 1041 -6.979952
## 72 1027 1031 1040 1044 -6.961929
## 73 1029 1033 1036 1042 -6.399282
## 74 1029 1031 1038 1042 -6.398130
## 75 1029 1032 1038 1041 -6.395106
## 76 1028 1031 1039 1042 -6.381290
## 77 1028 1032 1039 1041 -6.377761
## 78 1029 1032 1036 1043 -6.370396
## 79 1029 1033 1037 1041 -6.369336
## 80 1029 1031 1037 1043 -6.345000
## 81 1028 1034 1036 1042 -6.342272
## 82 1026 1033 1039 1042 -6.339745
## 83 1027 1033 1039 1041 -6.330802
## 84 1028 1032 1036 1044 -6.315192
## 85 1028 1034 1037 1041 -6.312793
## 86 1026 1032 1039 1043 -6.309469
## 87 1027 1031 1039 1043 -6.306180
## 88 1026 1034 1038 1042 -6.299689
## 89 1028 1031 1037 1044 -6.291242
## 90 1027 1034 1038 1041 -6.290642
## 91 1026 1032 1038 1044 -6.271700
## 92 1027 1031 1038 1044 -6.268827
## 93 1027 1033 1036 1044 -6.268725
## 94 1027 1034 1036 1043 -6.265904
## 95 1026 1033 1037 1044 -6.249541
## 96 1026 1034 1037 1043 -6.246754
## 97 1029 1033 1036 1045 -5.720024
## 98 1029 1035 1038 1041 -5.714463
## 99 1028 1035 1039 1041 -5.714243
## 100 1029 1035 1036 1043 -5.710035
## 101 1029 1031 1038 1045 -5.708712
## 102 1028 1031 1039 1045 -5.708588
## 103 1026 1033 1039 1045 -5.694937
## 104 1026 1035 1039 1043 -5.685026
## 105 1028 1035 1036 1044 -5.675590
## 106 1028 1034 1036 1045 -5.671573
## 107 1026 1035 1038 1044 -5.650312
## 108 1026 1034 1038 1045 -5.646338
## 109 1029 1033 1040 1041 -5.626516
## 110 1030 1033 1039 1041 -5.623941
## 111 1029 1031 1040 1043 -5.611557
## 112 1030 1031 1039 1043 -5.608923
## 113 1030 1033 1036 1044 -5.588388
## 114 1028 1034 1040 1041 -5.580897
## 115 1028 1031 1040 1044 -5.580204
## 116 1030 1034 1038 1041 -5.578031
## 117 1030 1031 1038 1044 -5.577377
## 118 1030 1034 1036 1043 -5.573941
## 119 1026 1033 1040 1044 -5.567516
## 120 1026 1034 1040 1043 -5.553379MM (connected vs unconnected)
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected")Our first step in the data analysis involves filtering the data to isolate the relevant data. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure we filtered data the right way.
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i)plot.metaecos.points(filtered_data,
metaecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
meta-ecosystem on multiple occasions, we can develop mixed effect models
to examine how the connection influenced this meta-ecosystem variable.
To study the effects of connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
system nr as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | system nr)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | system nr)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | system nr)).
Unconnected meta-ecosystems are made of paired unconnected
ecosystems, which are paired randomly. However, how to pair unconnected
ecosystems can be done in multiple ways, as unconnected ecosystems did
not interact and therefore any combination between ecosystems would be
arbitrary. To make sure that the random combination we selected did not
bias our results, we run all the possible combinations of ecosystems
constituting unconnected meta-ecosystems. The ecosystem combinations are
into the objects unconnected_combinations_sets (Data >
Meta-ecosystems). We therefore compute a p-value for each unconnected
ecosystems combination, creating a p-value distribution. We keep as
p-value of the comparison the mean of such distributions.
Click to view the code we used to computed the p-values
If you see “Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel = ## 1e-15, : unused control arguments ignored”, Ignore it. It just means that you didn’t pass the control argument to the Nelder_Mead optimiser, so it uses the default.
unconnected_combinations_sets_filtered = unconnected_combinations_sets %>%
filter(disturbance == disturbance_global_input,
metaecosystem_type %in% metaecosystem_type_i)
n_sets = unconnected_combinations_sets_filtered %>%
pull(set) %>%
max()
iterated_results_table = data.frame(Response = as.character(NA),
Levels = as.character(NA),
ΔAIC_full = NA,
p_full = NA,
ΔR2_full = NA,
ΔAIC_fix = NA,
p_fix = NA,
ΔR2_fix = NA,
combination_set = NA,
system_nr_unconnected_systems = as.character(NA)) %>%
slice(-1)
for (set_input in 1:n_sets) {
system_nr_unconnected_systems_input = unconnected_combinations_sets_filtered %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
connection == "unconnected",
set == set_input) %>%
pull(system_nr)
filtered_data = ds_metaecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
metaecosystem_type %in% metaecosystem_type_i,
connection == "connected" |
(connection == "unconnected" &
system_nr %in% system_nr_unconnected_systems_input))
null_model = lmer(
get(response_variable) ~
day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
full_model = lmer(
get(response_variable) ~
day +
connection +
connection:day +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
reduced_model = lmer(
get(response_variable) ~
day +
connection +
(day | system_nr),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = optimizer_input,
optCtrl = list(method = method_input)))
model_stats_fixed = compute.model.stats(reduced_model,
null_model,
"mixed_model")
iterated_results_table = fill.results.table(iterated_results_table,
response_variable,
metaecosystem_type_i,
model_stats_full,
model_stats_fixed)
iterated_results_table$set[nrow(iterated_results_table)] =
set_input
iterated_results_table$system_nr_unconnected_systems[nrow(iterated_results_table)] =
paste(system_nr_unconnected_systems_input, collapse = " ")
}## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored## Warning in (function (iprint = 0L, maxfun = 10000L, FtolAbs = 1e-05, FtolRel =
## 1e-15, : unused control arguments ignored
Full vs null model
Click to view p-value of the comparison between full and null model
model_stats_full = data.frame(
deltaAIC = mean(iterated_results_table$ΔAIC_full),
p_value = mean(iterated_results_table$p_full),
R2 = NA
)
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.3 0.167 noneClick to view the ΔAIC and p-value distributions of the comparison between full and null models
hist(iterated_results_table$ΔAIC_full, main = "Distribution of ΔAIC of the full model.") 
hist(iterated_results_table$p_full, main = "Distribution of p-values of the full model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_full) %>%
arrange(ΔAIC_full)## system_nr_unconnected_systems ΔAIC_full
## 1 1056 1065 -0.62042593
## 2 1065 1056 -0.62042593
## 3 1058 1062 -0.49794844
## 4 1062 1058 -0.49794844
## 5 1056 1064 -0.26493674
## 6 1064 1056 -0.26493674
## 7 1059 1061 -0.20354500
## 8 1061 1059 -0.20354500
## 9 1057 1062 -0.19138169
## 10 1062 1057 -0.19138169
## 11 1057 1065 0.02135567
## 12 1065 1057 0.02135567
## 13 1058 1064 0.05043751
## 14 1064 1058 0.05043751
## 15 1059 1060 0.10548001
## 16 1060 1059 0.10548001
## 17 1059 1063 0.34923867
## 18 1063 1059 0.34923867
## 19 1060 1065 0.74571276
## 20 1065 1060 0.74571276
## 21 1061 1064 0.76203591
## 22 1064 1061 0.76203591
## 23 1062 1063 0.84585905
## 24 1063 1062 0.84585905
## 25 1058 1060 1.20377042
## 26 1060 1058 1.20377042
## 27 1057 1061 1.22459781
## 28 1061 1057 1.22459781
## 29 1056 1063 1.24283225
## 30 1063 1056 1.24283225
Reduced vs null model
Click to view the ΔAIC and p-value distributions of the comparison between reduced and null models
model_stats_fixed = data.frame(deltaAIC = mean(iterated_results_table$ΔAIC_fix),
p_value = mean(iterated_results_table$p_fix),
R2 = NA)
model_stats_fixed %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.9 0.356 noneClick to view the ΔAIC and p-value distributions of the comparison between reduced and null models
hist(iterated_results_table$ΔAIC_fix, main = "Distribution of ΔAIC of the reduced model.") 
hist(iterated_results_table$p_fix, main = "Distribution of p-values of the reduced model.") 
Click to view which unconnected meta-ecosystem numbers produced which AIC in the comparison between full and null model
iterated_results_table %>%
select(system_nr_unconnected_systems,
ΔAIC_fix) %>%
arrange(ΔAIC_fix)## system_nr_unconnected_systems ΔAIC_fix
## 1 1056 1065 -0.6946471
## 2 1065 1056 -0.6946471
## 3 1058 1062 -0.6033386
## 4 1062 1058 -0.6033386
## 5 1059 1061 -0.4184667
## 6 1061 1059 -0.4184667
## 7 1056 1064 0.8085298
## 8 1064 1056 0.8085298
## 9 1057 1062 1.0136835
## 10 1062 1057 1.0136835
## 11 1061 1064 1.1260933
## 12 1064 1061 1.1260933
## 13 1058 1064 1.1906671
## 14 1064 1058 1.1906671
## 15 1059 1060 1.2606299
## 16 1060 1059 1.2606299
## 17 1057 1065 1.3250017
## 18 1065 1057 1.3250017
## 19 1060 1065 1.3423113
## 20 1065 1060 1.3423113
## 21 1057 1061 1.4404786
## 22 1061 1057 1.4404786
## 23 1062 1063 1.4615803
## 24 1063 1062 1.4615803
## 25 1058 1060 1.5149510
## 26 1060 1058 1.5149510
## 27 1056 1063 1.5979996
## 28 1063 1056 1.5979996
## 29 1059 1063 1.6311258
## 30 1063 1059 1.6311258All ecosystems
ecosystem_type_i = c("Small unconnected",
"Medium unconnected",
"Large unconnected",
"Small connected to small",
"Small connected to large",
"Medium connected to medium",
"Large connected to small",
"Large connected to large")BEF
ds_ecosystems %>%
filter(is.na(species_richness) != TRUE) %>%
ggplot(aes(x = species_richness,
y = bioarea_mm2_per_ml)) +
geom_point() +
xlim(0, length(protist_species)) +
labs(x = axis_names$axis_name[axis_names$variable == "species_richness"],
y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"))
ds_ecosystems %>%
filter(is.na(shannon) != TRUE) %>%
ggplot(aes(x = shannon,
y = bioarea_mm2_per_ml)) +
geom_point() +
labs(x = axis_names$axis_name[axis_names$variable == "shannon"],
y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"))
ds_ecosystems %>%
filter(is.na(evenness_pielou) != TRUE) %>%
ggplot(aes(x = evenness_pielou,
y = bioarea_mm2_per_ml)) +
geom_point() +
labs(x = axis_names$axis_name[axis_names$variable == "evenness_pielou"],
y = axis_names$axis_name[axis_names$variable == "bioarea_mm2_per_ml"]) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"))
\(S\) vs \(M\) vs \(L\)
ecosystem_type_i = c("Small unconnected",
"Medium unconnected",
"Large unconnected")Shannon
response_variable = "shannon"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
save_results_in_table = TRUE
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point >= first_time_point_model,
time_point <= last_time_point_model,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
full_model = lmer(
get(response_variable) ~
ecosystem_size * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_size + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))## Warning: Model failed to converge with 1 negative eigenvalue: -1.5e+01Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -35 < 0.001 **** very strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 62.9 86.4 -21.4 42.9 68
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.37 -0.62 0.05 0.68 2.38
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-11 5e-06
## day 2e-14 1e-07 -1.00
## Residual 1e-01 3e-01
## Number of obs: 78, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1e+00 2e-01 8e+01 9.0 9e-14 ***
## ecosystem_sizeMedium -3e-01 2e-01 8e+01 -1.2 0.2
## ecosystem_sizeSmall 1e-01 3e-01 8e+01 0.5 0.6
## day -7e-04 9e-03 8e+01 -0.1 0.9
## ecosystem_sizeMedium:day 3e-03 1e-02 8e+01 0.3 0.8
## ecosystem_sizeSmall:day -7e-02 1e-02 8e+01 -4.8 6e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S day ecs_M:
## ecsystm_szM -0.707
## ecsystm_szS -0.622 0.440
## day -0.935 0.661 0.582
## ecsystm_sM: 0.661 -0.935 -0.411 -0.707
## ecsystm_sS: 0.541 -0.382 -0.931 -0.578 0.409
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -20.2 < 0.001 **** very strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 77.7 96.5 -30.8 61.7 70
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.90 -0.62 -0.05 0.66 2.27
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.51
## day 8e-04 0.03 -1.00
## Residual 1e-01 0.33
## Number of obs: 78, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.778 0.179 14.000 10 1e-07 ***
## ecosystem_sizeMedium -0.220 0.084 62.158 -3 0.01 *
## ecosystem_sizeSmall -1.093 0.099 54.140 -11 2e-15 ***
## day -0.017 0.009 12.450 -2 0.09 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.235
## ecsystm_szS -0.277 0.424
## day -0.943 0.000 0.082
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
save_results_in_table = TRUE
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point >= first_time_point_model,
time_point <= last_time_point_model,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
full_model = lmer(
get(response_variable) ~
ecosystem_size * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_size + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -33.7 < 0.001 **** very strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 202.4 226.7 -91.2 182.4 74
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.36 -0.72 -0.01 0.53 2.48
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.131
## day 5e-05 0.007 -1.00
## Residual 5e-01 0.715
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.94 0.37 15.56 15.9 5e-11 ***
## ecosystem_sizeMedium -1.63 0.53 15.56 -3.1 0.007 **
## ecosystem_sizeSmall -4.14 0.56 15.56 -7.4 2e-06 ***
## day -0.16 0.02 14.38 -8.3 8e-07 ***
## ecosystem_sizeMedium:day 0.02 0.03 14.38 0.8 0.421
## ecosystem_sizeSmall:day 0.08 0.03 14.38 2.9 0.011 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S day ecs_M:
## ecsystm_szM -0.707
## ecsystm_szS -0.667 0.471
## day -0.937 0.662 0.624
## ecsystm_sM: 0.662 -0.937 -0.442 -0.707
## ecsystm_sS: 0.624 -0.442 -0.937 -0.667 0.471
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -30.8 < 0.001 **** very strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 205.3 224.7 -94.6 189.3 76
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1 -0.8 -0.1 0.7 2.4
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.419 0.65
## day 0.001 0.04 -1.00
## Residual 0.511 0.72
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.35 0.30 17.96 18 7e-13 ***
## ecosystem_sizeMedium -1.22 0.18 69.16 -7 7e-09 ***
## ecosystem_sizeSmall -2.60 0.20 69.16 -13 <2e-16 ***
## day -0.13 0.01 14.02 -9 6e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.309
## ecsystm_szS -0.292 0.471
## day -0.899 0.000 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
save_results_in_table = TRUE
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point >= first_time_point_model,
time_point <= last_time_point_model,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable)
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
full_model = lmer(
get(response_variable) ~
ecosystem_size * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_size + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -37.8 < 0.001 **** very strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 306.0 330.3 -143.0 286.0 74
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.52 -0.60 0.04 0.74 2.12
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 1e-14 1e-07 NaN
## Residual 2e+00 1e+00
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.17 0.68 84.00 10.5 <2e-16 ***
## ecosystem_sizeMedium 0.33 0.97 84.00 0.3 0.74
## ecosystem_sizeSmall -1.09 1.02 84.00 -1.1 0.29
## day -0.02 0.04 84.00 -0.5 0.60
## ecosystem_sizeMedium:day -0.09 0.05 84.00 -1.8 0.08 .
## ecosystem_sizeSmall:day -0.22 0.05 84.00 -4.1 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S day ecs_M:
## ecsystm_szM -0.707
## ecsystm_szS -0.667 0.471
## day -0.935 0.661 0.623
## ecsystm_sM: 0.661 -0.935 -0.441 -0.707
## ecsystm_sS: 0.623 -0.441 -0.935 -0.667 0.471
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -28.7 < 0.001 **** very strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 315.1 334.6 -149.6 299.1 76
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.6 -0.1 0.5 2.4
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1.795 1.34
## day 0.005 0.07 -1.00
## Residual 1.875 1.37
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.89 0.59 16.76 15 3e-11 ***
## ecosystem_sizeMedium -1.30 0.35 66.58 -4 5e-04 ***
## ecosystem_sizeSmall -5.08 0.38 66.58 -14 <2e-16 ***
## day -0.11 0.03 14.06 -4 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.302
## ecsystm_szS -0.284 0.471
## day -0.904 0.000 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
save_results_in_table = TRUE
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point >= first_time_point_model,
time_point <= last_time_point_model,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
full_model = lmer(
get(response_variable) ~
ecosystem_size * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_size + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -37.6 < 0.001 **** very strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -64.1 -41.1 42.1 -84.1 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6 -0.6 0.2 0.5 3.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 1e-17 4e-09 NaN
## Residual 2e-02 1e-01
## Number of obs: 74, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8e-01 7e-02 7e+01 10.7 <2e-16 ***
## ecosystem_sizeMedium -2e-01 1e-01 7e+01 -2.1 0.04 *
## ecosystem_sizeSmall 5e-01 1e-01 7e+01 4.0 1e-04 ***
## day 5e-04 4e-03 7e+01 0.1 0.88
## ecosystem_sizeMedium:day 1e-02 5e-03 7e+01 2.2 0.03 *
## ecosystem_sizeSmall:day -5e-02 6e-03 7e+01 -7.5 1e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S day ecs_M:
## ecsystm_szM -0.707
## ecsystm_szS -0.623 0.441
## day -0.935 0.661 0.583
## ecsystm_sM: 0.661 -0.935 -0.412 -0.707
## ecsystm_sS: 0.563 -0.398 -0.919 -0.602 0.426
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -11.5 < 0.001 **** very strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -38.1 -19.6 27.0 -54.1 66
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2 -0.5 0.1 0.5 2.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-01 0.44
## day 6e-04 0.02 -1.00
## Residual 2e-02 0.14
## Number of obs: 74, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 9e-01 1e-01 1e+01 7 8e-06 ***
## ecosystem_sizeMedium -5e-04 4e-02 6e+01 0 1.0
## ecosystem_sizeSmall -4e-01 5e-02 5e+01 -9 1e-11 ***
## day -8e-03 7e-03 1e+01 -1 0.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.139
## ecsystm_szS -0.142 0.389
## day -0.981 0.000 0.035
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
save_results_in_table = TRUE
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point >= first_time_point_model,
time_point <= last_time_point_model,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
full_model = lmer(
get(response_variable) ~
ecosystem_size * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_size + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.2 0.057 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1285.6 1309.2 -632.8 1265.6 68
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.85 -0.45 0.04 0.59 2.84
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e+05 310
## day 3e+01 6 -1.00
## Residual 6e+05 782
## Number of obs: 78, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3337 426 23 7.8 6e-08 ***
## ecosystem_sizeMedium -21 602 23 0.0 0.97
## ecosystem_sizeSmall -1222 680 28 -1.8 0.08 .
## day -7 21 44 -0.3 0.73
## ecosystem_sizeMedium:day 31 30 44 1.1 0.30
## ecosystem_sizeSmall:day 66 36 50 1.8 0.08 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S day ecs_M:
## ecsystm_szM -0.707
## ecsystm_szS -0.626 0.443
## day -0.916 0.648 0.574
## ecsystm_sM: 0.648 -0.916 -0.406 -0.707
## ecsystm_sS: 0.531 -0.375 -0.913 -0.579 0.410
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -2 0.05 * weakClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1284.8 1303.7 -634.4 1268.8 70
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.98 -0.34 0.05 0.55 2.75
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e+05 434
## day 2e+02 14 -1.00
## Residual 6e+05 800
## Number of obs: 78, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2846 314 21 9.0 1e-08 ***
## ecosystem_sizeMedium 576 235 11 2.5 0.03 *
## ecosystem_sizeSmall -63 273 14 -0.2 0.82
## day 18 14 22 1.3 0.20
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.373
## ecsystm_szS -0.419 0.429
## day -0.850 0.000 0.116
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Auto/Hetero
response_variable = "auto_hetero_ratio"We want to know whether the size of ecosystems influenced this response variable. We only look at unconnected ecosystems so that the effects of connection don’t confound the effects of ecosystem size. We first start from plotting how this response variable changed in different sizes throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
save_results_in_table = TRUE
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(metaecosystem == "no",
time_point >= first_time_point_model,
time_point <= last_time_point_model,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how ecosystem size influenced this variable. To study the
effects of ecosystem size we compare two models to a null model using
ANOVA: a full model and a reduced model. In all models, we treat culture
ID as having a random effect on how the slope and intercept of the
relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of size with time
(Response variable ~ size * day + (day | culture ID)), the
reduced model contains the size but without the interaction with time
(Response variable ~ size + day + (day | culture ID)), and
the null model doesn’t contain the size at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem size had an
effect.
full_model = lmer(
get(response_variable) ~
ecosystem_size * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_size + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -3.1 0.026 ** moderateClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -2.3 21.3 11.2 -22.3 68
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.4 -0.1 0.3 6.2
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.14
## day 1e-04 0.01 -1.00
## Residual 4e-02 0.20
## Number of obs: 78, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.153 0.120 22.622 -1 0.215
## ecosystem_sizeMedium 0.218 0.170 22.622 1 0.211
## ecosystem_sizeSmall 0.317 0.189 26.479 2 0.106
## day 0.024 0.007 15.956 3 0.005 **
## ecosystem_sizeMedium:day -0.022 0.010 15.956 -2 0.046 *
## ecosystem_sizeSmall:day -0.030 0.012 21.388 -3 0.017 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S day ecs_M:
## ecsystm_szM -0.707
## ecsystm_szS -0.633 0.448
## day -0.943 0.667 0.597
## ecsystm_sM: 0.667 -0.943 -0.422 -0.707
## ecsystm_sS: 0.579 -0.410 -0.944 -0.614 0.434
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.4 0.109 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_size + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 0.3 19.2 7.8 -15.7 70
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.3 -0.1 0.3 6.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-02 0.22
## day 3e-04 0.02 -1.00
## Residual 4e-02 0.20
## Number of obs: 78, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.091 0.093 23.009 1 0.34
## ecosystem_sizeMedium -0.122 0.056 42.120 -2 0.04 *
## ecosystem_sizeSmall -0.146 0.062 50.826 -2 0.02 *
## day 0.008 0.005 15.176 1 0.17
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecsy_M ecsy_S
## ecsystm_szM -0.303
## ecsystm_szS -0.312 0.452
## day -0.903 0.000 0.042
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small unconnected"
## [1] "Medium unconnected"
## [1] "Large unconnected"
\(S_{L}\) vs \(S\)
ecosystem_type_i = c("Small connected to large",
"Small unconnected")Shannon
response_variable = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) ## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -5.4 0.009 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 62.7 77.6 -23.3 46.7 40
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.5 0.1 0.6 2.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-04 0.023
## day 4e-05 0.006 -1.00
## Residual 1e-01 0.382
## Number of obs: 48, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.017 0.197 38.690 10.2 1e-12
## ecosystem_typeSmall unconnected -0.391 0.317 39.094 -1.2 0.2
## day -0.065 0.011 24.167 -6.1 2e-06
## ecosystem_typeSmall unconnected:day -0.007 0.018 30.372 -0.4 0.7
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## day ***
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.622
## day -0.913 0.568
## ecsystm_Su: 0.533 -0.915 -0.584
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.2 0.002 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 60.8 73.9 -23.4 46.8 41
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.5 0.1 0.6 2.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-04 0.023
## day 4e-05 0.006 -1.00
## Residual 1e-01 0.383
## Number of obs: 48, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.058 0.167 43.391 12 9e-16 ***
## ecosystem_typeSmall unconnected -0.504 0.128 14.192 -4 0.001 **
## day -0.068 0.009 27.070 -8 2e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.394
## day -0.876 0.103
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -3.9 0.019 ** moderateClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 113.7 129.6 -48.8 97.7 46
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1 -0.6 0.0 0.5 3.3
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-11 5e-06
## day 1e-14 1e-07 -1.00
## Residual 4e-01 6e-01
## Number of obs: 54, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.04 0.31 54.00 10 1e-13
## ecosystem_typeSmall unconnected -1.24 0.46 54.00 -3 0.009
## day -0.12 0.02 54.00 -8 7e-10
## ecosystem_typeSmall unconnected:day 0.04 0.02 54.00 2 0.068
##
## (Intercept) ***
## ecosystem_typeSmall unconnected **
## day ***
## ecosystem_typeSmall unconnected:day .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.667
## day -0.935 0.623
## ecsystm_Su: 0.623 -0.935 -0.667
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -2.6 0.032 ** moderateClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 115.0 128.9 -50.5 101.0 47
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9 -0.7 -0.1 0.4 3.4
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e-02 0.24
## day 1e-04 0.01 -1.00
## Residual 4e-01 0.61
## Number of obs: 54, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.68 0.26 9.52 10 2e-06 ***
## ecosystem_typeSmall unconnected -0.43 0.17 44.23 -2 0.01 *
## day -0.10 0.01 11.58 -8 6e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.290
## day -0.900 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.3 0.003 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 207.1 223.0 -95.6 191.1 46
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.06 -0.56 0.07 0.41 2.34
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 6e-15 8e-08 NaN
## Residual 2e+00 1e+00
## Number of obs: 54, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.12 0.73 54.00 11.1 1e-15
## ecosystem_typeSmall unconnected -2.04 1.10 54.00 -1.9 0.07
## day -0.27 0.04 54.00 -7.0 4e-09
## ecosystem_typeSmall unconnected:day 0.03 0.06 54.00 0.5 0.60
##
## (Intercept) ***
## ecosystem_typeSmall unconnected .
## day ***
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.667
## day -0.935 0.623
## ecsystm_Su: 0.623 -0.935 -0.667
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -9 0.001 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 205.4 219.3 -95.7 191.4 47
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.0 -0.6 0.1 0.5 2.2
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 2e-14 1e-07 NaN
## Residual 2e+00 1e+00
## Number of obs: 54, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.88 0.57 54.00 14 <2e-16 ***
## ecosystem_typeSmall unconnected -1.50 0.39 54.00 -4 3e-04 ***
## day -0.25 0.03 54.00 -9 4e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.302
## day -0.891 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) ## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -23.9 < 0.001 **** very strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -17.4 -4.5 16.7 -33.4 29
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2 -0.5 0.0 0.4 2.7
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-03 0.047
## day 4e-06 0.002 -1.00
## Residual 2e-02 0.153
## Number of obs: 37, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.820 0.089 10.000 9.2 3e-06
## ecosystem_typeSmall unconnected 0.393 0.135 10.380 2.9 0.01
## day 0.004 0.005 24.672 0.9 0.39
## ecosystem_typeSmall unconnected:day -0.050 0.007 23.986 -6.6 7e-07
##
## (Intercept) ***
## ecosystem_typeSmall unconnected *
## day
## ecosystem_typeSmall unconnected:day ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.660
## day -0.931 0.614
## ecsystm_Su: 0.629 -0.920 -0.676
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -8.4 0.001 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -2.0 9.3 8.0 -16.0 30
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.77 -0.50 -0.06 0.48 2.39
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-01 0.46
## day 6e-04 0.02 -1.00
## Residual 2e-02 0.16
## Number of obs: 37, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.236 0.168 7.497 7 1e-04 ***
## ecosystem_typeSmall unconnected -0.537 0.057 22.910 -10 2e-09 ***
## day -0.018 0.009 8.949 -2 0.07 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.113
## day -0.977 -0.022
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) ## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))## Warning: Model failed to converge with 1 negative eigenvalue: -1.3e-02null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))## Warning: Model failed to converge with 1 negative eigenvalue: -3.0e-02Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2.7 0.512 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 827.3 842.3 -405.7 811.3 40
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.79 -0.38 -0.03 0.62 1.77
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 8e+03 87
## day 2e+03 49 -1.00
## Residual 1e+06 982
## Number of obs: 48, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2364 507 37 4.7 4e-05
## ecosystem_typeSmall unconnected -325 815 38 -0.4 0.69
## day 83 34 11 2.5 0.03
## ecosystem_typeSmall unconnected:day -20 56 15 -0.4 0.72
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## day *
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.621
## day -0.767 0.477
## ecsystm_Su: 0.468 -0.797 -0.609
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.9 0.284 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 825.5 838.6 -405.8 811.5 41
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.79 -0.46 -0.03 0.58 1.78
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0
## day 2e+03 44 NaN
## Residual 1e+06 983
## Number of obs: 48, groups: culture_ID, 9
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2451 451 40 5 3e-06 ***
## ecosystem_typeSmall unconnected -561 511 11 -1 0.30
## day 76 26 15 3 0.01 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.481
## day -0.665 -0.017
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small connected to large"
## [1] "Small unconnected"
\(S_{L}\) vs \(S_{S}\)
ecosystem_type_i = c("Small connected to large",
"Small connected to small")Shannon
response_variable = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -2.2 0.045 ** moderateClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 74.2 93.7 -29.1 58.2 76
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.11 -0.47 0.01 0.68 2.55
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.15
## day 2e-04 0.01 -1.00
## Residual 1e-01 0.32
## Number of obs: 84, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2.017 0.179 28.034 11.2
## ecosystem_typeSmall connected to small -0.177 0.224 29.392 -0.8
## day -0.065 0.011 15.965 -6.0
## ecosystem_typeSmall connected to small:day -0.004 0.014 17.612 -0.3
## Pr(>|t|)
## (Intercept) 7e-12 ***
## ecosystem_typeSmall connected to small 0.4
## day 2e-05 ***
## ecosystem_typeSmall connected to small:day 0.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts day
## ecsyst_Scts -0.800
## day -0.920 0.736
## ecsys_Scts: 0.727 -0.923 -0.790
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -4.1 0.013 ** moderateClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 72.3 89.3 -29.2 58.3 77
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.09 -0.48 0.02 0.70 2.59
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.16
## day 2e-04 0.01 -1.00
## Residual 1e-01 0.32
## Number of obs: 84, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2.051 0.123 52.993 17
## ecosystem_typeSmall connected to small -0.231 0.086 26.679 -3
## day -0.067 0.007 18.757 -10
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall connected to small 0.01 *
## day 4e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts
## ecsyst_Scts -0.486
## day -0.822 0.028
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.6 0.06 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 158.7 178.7 -71.4 142.7 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.6 0.0 0.5 3.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-02 0.23
## day 9e-05 0.01 -1.00
## Residual 3e-01 0.53
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3.04 0.29 16.95 10
## ecosystem_typeSmall connected to small -0.82 0.36 16.95 -2
## day -0.12 0.01 28.24 -8
## ecosystem_typeSmall connected to small:day 0.03 0.02 28.24 2
## Pr(>|t|)
## (Intercept) 8e-09 ***
## ecosystem_typeSmall connected to small 0.03 *
## day 8e-09 ***
## ecosystem_typeSmall connected to small:day 0.09 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts day
## ecsyst_Scts -0.816
## day -0.940 0.768
## ecsys_Scts: 0.768 -0.940 -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.6 0.104 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 159.7 177.2 -72.8 145.7 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2 -0.7 0.0 0.5 3.7
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-01 0.34
## day 2e-04 0.02 -1.00
## Residual 3e-01 0.53
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2.637 0.198 19.628 13
## ecosystem_typeSmall connected to small -0.218 0.123 54.872 -2
## day -0.098 0.009 20.642 -11
## Pr(>|t|)
## (Intercept) 3e-11 ***
## ecosystem_typeSmall connected to small 0.08 .
## day 6e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts
## ecsyst_Scts -0.414
## day -0.862 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.6 0.003 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 294.1 314.1 -139.0 278.1 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.58 -0.65 0.01 0.43 2.93
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 4e-13 6e-07 NaN
## Residual 1e+00 1e+00
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 8.12 0.58 90.00 14
## ecosystem_typeSmall connected to small -1.93 0.71 90.00 -3
## day -0.27 0.03 90.00 -9
## ecosystem_typeSmall connected to small:day 0.06 0.04 90.00 2
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall connected to small 0.008 **
## day 1e-13 ***
## ecosystem_typeSmall connected to small:day 0.132
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts day
## ecsyst_Scts -0.816
## day -0.935 0.763
## ecsys_Scts: 0.763 -0.935 -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.3 0.002 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 294.3 311.8 -140.2 280.3 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.43 -0.74 0.03 0.26 2.95
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 6e-14 3e-07 NaN
## Residual 1e+00 1e+00
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 7.44 0.38 90.00 20
## ecosystem_typeSmall connected to small -0.92 0.26 90.00 -4
## day -0.23 0.02 90.00 -13
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeSmall connected to small 6e-04 ***
## day <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts
## ecsyst_Scts -0.448
## day -0.836 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.1 0.004 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -15.9 1.8 15.9 -31.9 59
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.13 -0.61 0.03 0.52 2.23
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.118
## day 9e-05 0.009 -1.00
## Residual 3e-02 0.180
## Number of obs: 67, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.821 0.117 27.360 7.0
## ecosystem_typeSmall connected to small 0.383 0.142 26.723 2.7
## day 0.004 0.007 16.874 0.6
## ecosystem_typeSmall connected to small:day -0.034 0.009 16.314 -3.7
## Pr(>|t|)
## (Intercept) 1e-07 ***
## ecosystem_typeSmall connected to small 0.012 *
## day 0.567
## ecosystem_typeSmall connected to small:day 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts day
## ecsyst_Scts -0.823
## day -0.940 0.773
## ecsys_Scts: 0.775 -0.938 -0.824
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.3 0.187 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -8.6 6.9 11.3 -22.6 60
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4 -0.6 0.0 0.5 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e-02 0.23
## day 3e-04 0.02 -1.00
## Residual 3e-02 0.18
## Number of obs: 67, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.125 0.092 23.749 12
## ecosystem_typeSmall connected to small -0.084 0.051 45.033 -2
## day -0.018 0.006 15.210 -3
## Pr(>|t|)
## (Intercept) 1e-11 ***
## ecosystem_typeSmall connected to small 0.11
## day 0.01 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts
## ecsyst_Scts -0.363
## day -0.895 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.4 0.068 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1445.3 1464.8 -714.7 1429.3 76
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6 -0.4 0.1 0.6 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 7e+04 272
## day 1e+03 39 -1.00
## Residual 1e+06 1129
## Number of obs: 84, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2364 593 50 4
## ecosystem_typeSmall connected to small 958 745 51 1
## day 83 35 21 2
## ecosystem_typeSmall connected to small:day -94 44 23 -2
## Pr(>|t|)
## (Intercept) 2e-04 ***
## ecosystem_typeSmall connected to small 0.20
## day 0.03 *
## ecosystem_typeSmall connected to small:day 0.04 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Scts day
## ecsyst_Scts -0.797
## day -0.896 0.714
## ecsys_Scts: 0.702 -0.900 -0.784
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.7 0.246 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1447.4 1464.4 -716.7 1433.4 77
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6 -0.5 0.1 0.6 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e+05 525
## day 3e+03 54 -1.00
## Residual 1e+06 1142
## Number of obs: 84, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3222 441 58 7
## ecosystem_typeSmall connected to small -421 321 25 -1
## day 25 24 18 1
## Pr(>|t|)
## (Intercept) 9e-10 ***
## ecosystem_typeSmall connected to small 0.2
## day 0.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Scts
## ecsyst_Scts -0.502
## day -0.805 0.024
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small connected to large"
## [1] "Small connected to small"
\(S_{S}\) vs \(S\)
ecosystem_type_i = c("Small connected to small",
"Small unconnected")Shannon
response_variable = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) ## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -2.4 0.04 ** moderateClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 62.3 80.5 -23.2 46.3 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1 -0.5 0.0 0.7 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.12
## day 1e-04 0.01 -1.00
## Residual 1e-01 0.32
## Number of obs: 72, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.834 0.130 25.655 14.1 1e-13
## ecosystem_typeSmall unconnected -0.203 0.253 28.212 -0.8 0.4
## day -0.068 0.008 16.552 -8.7 1e-07
## ecosystem_typeSmall unconnected:day -0.004 0.016 20.778 -0.3 0.8
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## day ***
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.516
## day -0.928 0.479
## ecsystm_Su: 0.469 -0.927 -0.505
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -4.4 0.012 ** moderateClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 60.4 76.3 -23.2 46.4 65
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1 -0.5 0.0 0.7 2.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.13
## day 1e-04 0.01 -1.00
## Residual 1e-01 0.32
## Number of obs: 72, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.851 0.115 30.052 16 3e-16 ***
## ecosystem_typeSmall unconnected -0.267 0.095 23.137 -3 0.01 **
## day -0.069 0.007 17.719 -10 8e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.247
## day -0.907 0.033
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.1 0.142 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 111.5 130.9 -47.7 95.5 76
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.7 0.0 0.6 4.2
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 8e-03 0.087
## day 1e-05 0.004 -1.00
## Residual 2e-01 0.426
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.218 0.157 16.456 14.1 1e-10
## ecosystem_typeSmall unconnected -0.421 0.295 16.456 -1.4 0.2
## day -0.087 0.008 31.270 -10.7 5e-12
## ecosystem_typeSmall unconnected:day 0.012 0.015 31.270 0.8 0.4
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## day ***
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.535
## day -0.936 0.500
## ecsystm_Su: 0.500 -0.936 -0.535
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.3 0.071 * weakClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 110.1 127.2 -48.1 96.1 77
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3 -0.7 -0.1 0.6 4.3
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.119
## day 3e-05 0.005 -1.00
## Residual 2e-01 0.427
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.153 0.138 16.579 16 3e-11 ***
## ecosystem_typeSmall unconnected -0.196 0.104 60.171 -2 0.06 .
## day -0.084 0.007 27.861 -12 1e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.215
## day -0.915 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.4 0.069 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 266.5 286.0 -125.3 250.5 76
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.7 -0.1 0.5 2.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 7e-14 3e-07 NaN
## Residual 1e+00 1e+00
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.18 0.39 84.00 15.8 <2e-16
## ecosystem_typeSmall unconnected -0.11 0.73 84.00 -0.1 0.9
## day -0.21 0.02 84.00 -10.3 <2e-16
## ecosystem_typeSmall unconnected:day -0.03 0.04 84.00 -0.7 0.5
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## day ***
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.535
## day -0.935 0.500
## ecsystm_Su: 0.500 -0.935 -0.535
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -2.9 0.027 ** moderateClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 265.0 282.0 -125.5 251.0 77
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.7 -0.1 0.4 2.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 7e-15 8e-08 NaN
## Residual 1e+00 1e+00
## Number of obs: 84, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.32 0.34 84.00 19 <2e-16 ***
## ecosystem_typeSmall unconnected -0.58 0.26 84.00 -2 0.03 *
## day -0.22 0.02 84.00 -13 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.219
## day -0.912 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) ## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))## Warning: Model failed to converge with 1 negative eigenvalue: -1.9e+00Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -8 0.003 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 11.4 27.9 2.3 -4.6 50
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.36 -0.58 0.04 0.78 1.96
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 9e-03 0.095
## day 5e-05 0.007 -1.00
## Residual 5e-02 0.227
## Number of obs: 58, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.210 0.094 28.012 13 3e-13
## ecosystem_typeSmall unconnected 0.008 0.180 31.856 0 1.0
## day -0.030 0.006 15.767 -5 7e-05
## ecosystem_typeSmall unconnected:day -0.016 0.010 18.860 -2 0.1
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## day ***
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.521
## day -0.928 0.483
## ecsystm_Su: 0.497 -0.920 -0.535
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.8 0.002 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 11.6 26.0 1.2 -2.4 51
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3 -0.7 -0.1 0.8 2.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.122
## day 8e-05 0.009 -1.00
## Residual 5e-02 0.229
## Number of obs: 58, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.280 0.085 26.147 15 2e-14 ***
## ecosystem_typeSmall unconnected -0.240 0.072 44.623 -3 0.002 **
## day -0.034 0.005 15.417 -7 5e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.179
## day -0.909 -0.030
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) ## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.9 0.35 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1233.5 1251.7 -608.8 1217.5 64
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.5 0.2 0.6 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-03 4e-02
## day 2e-06 1e-03 -1.00
## Residual 1e+06 1e+03
## Number of obs: 72, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3335 439 72 7.6 9e-11
## ecosystem_typeSmall unconnected -1226 857 72 -1.4 0.2
## day -12 24 72 -0.5 0.6
## ecosystem_typeSmall unconnected:day 71 49 72 1.4 0.2
##
## (Intercept) ***
## ecosystem_typeSmall unconnected
## day
## ecosystem_typeSmall unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su day
## ecsystm_tSu -0.512
## day -0.936 0.479
## ecsystm_Su: 0.460 -0.932 -0.492
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.9 0.806 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1233.5 1249.5 -609.8 1219.5 65
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.5 0.2 0.7 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 7e-04 3e-02
## day 2e-06 1e-03 -1.00
## Residual 1e+06 1e+03
## Number of obs: 72, groups: culture_ID, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3044 395 72 7.7 5e-11 ***
## ecosystem_typeSmall unconnected -77 314 72 -0.2 0.8
## day 5 21 72 0.3 0.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Su
## ecsystm_tSu -0.258
## day -0.918 0.065
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Small connected to small"
## [1] "Small unconnected"
\(L_{S}\) vs \(L\)
ecosystem_type_i = c("Large connected to small",
"Large unconnected")Shannon
response_variable = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1 0.22 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 34.0 50.7 -9.0 18.0 52
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.93 -0.65 -0.06 0.77 1.72
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.125
## day 6e-05 0.008 -1.00
## Residual 8e-02 0.276
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.224 0.153 16.644 8.0 4e-07
## ecosystem_typeLarge unconnected 0.257 0.216 16.644 1.2 0.3
## day 0.007 0.008 11.109 0.9 0.4
## ecosystem_typeLarge unconnected:day -0.008 0.012 11.109 -0.7 0.5
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.707
## day -0.943 0.667
## ecsystm_Lu: 0.667 -0.943 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.6 0.109 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 32.5 47.1 -9.2 18.5 53
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8 -0.7 -0.1 0.8 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-02 0.139
## day 8e-05 0.009 -1.00
## Residual 8e-02 0.276
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1e+00 1e-01 2e+01 11.2 9e-10 ***
## ecosystem_typeLarge unconnected 1e-01 7e-02 5e+01 1.6 0.1
## day 3e-03 6e-03 1e+01 0.6 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.312
## day -0.898 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = 'optimx',
optCtrl = list(method = 'nlminb')))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.5 0.003 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 168.5 185.3 -76.3 152.5 52
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.95 -0.70 -0.07 0.69 2.18
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.964 0.98
## day 0.002 0.05 -1.00
## Residual 0.656 0.81
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 4.76 0.61 10.04 7.9 1e-05
## ecosystem_typeLarge unconnected 1.18 0.86 10.04 1.4 0.2
## day -0.15 0.03 10.62 -5.0 5e-04
## ecosystem_typeLarge unconnected:day -0.01 0.04 10.62 -0.3 0.8
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day ***
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.707
## day -0.965 0.683
## ecsystm_Lu: 0.683 -0.965 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -9.5 0.001 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb"))
##
## AIC BIC logLik deviance df.resid
## 166.6 181.3 -76.3 152.6 53
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.91 -0.69 -0.07 0.70 2.17
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0.979 0.99
## day 0.002 0.05 -1.00
## Residual 0.656 0.81
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 4.88 0.44 11.29 11 2e-07 ***
## ecosystem_typeLarge unconnected 0.93 0.22 29.77 4 2e-04 ***
## day -0.15 0.02 10.60 -7 2e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.251
## day -0.935 0.000
## optimizer (optimx) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -5.6 0.008 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 198.3 215.1 -91.2 182.3 52
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.39 -0.72 0.05 0.89 2.13
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 8e-12 3e-06
## day 1e-14 1e-07 -1.00
## Residual 1e+00 1e+00
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6e+00 6e-01 6e+01 10.8 9e-16
## ecosystem_typeLarge unconnected 1e+00 8e-01 6e+01 1.2 0.2
## day -2e-02 3e-02 6e+01 -0.6 0.5
## ecosystem_typeLarge unconnected:day -6e-16 4e-02 6e+01 0.0 1.0
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.707
## day -0.935 0.661
## ecsystm_Lu: 0.661 -0.935 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.6 0.002 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 196.3 211.0 -91.2 182.3 53
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.39 -0.72 0.05 0.89 2.13
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 8e-12 3e-06
## day 1e-14 1e-07 -1.00
## Residual 1e+00 1e+00
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.17 0.43 60.00 14.4 <2e-16 ***
## ecosystem_typeLarge unconnected 1.00 0.29 60.00 3.5 9e-04 ***
## day -0.02 0.02 60.00 -0.9 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.334
## day -0.881 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2.9 0.581 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -71.4 -54.7 43.7 -87.4 52
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6 -0.6 0.3 0.7 1.5
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-03 0.050
## day 1e-05 0.003 -1.00
## Residual 1e-02 0.115
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.673 0.063 18.728 10.7 2e-09
## ecosystem_typeLarge unconnected 0.084 0.089 18.728 0.9 0.4
## day 0.006 0.003 11.621 1.7 0.1
## ecosystem_typeLarge unconnected:day -0.005 0.005 11.621 -1.1 0.3
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.707
## day -0.942 0.666
## ecsystm_Lu: 0.666 -0.942 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2 0.893 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -72.4 -57.7 43.2 -86.4 53
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.6 0.2 0.8 1.5
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-03 0.063
## day 2e-05 0.004 -1.00
## Residual 1e-02 0.115
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.717 0.049 19.377 14.7 5e-12 ***
## ecosystem_typeLarge unconnected -0.004 0.030 44.928 -0.1 0.9
## day 0.003 0.003 10.997 1.2 0.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.309
## day -0.900 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.5 0.291 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 971.3 988.0 -477.6 955.3 52
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.6 -0.1 0.5 2.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e+04 170
## day 1e+02 12 -1.00
## Residual 5e+05 688
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3627.2 362.0 29.3 10.0 6e-11
## ecosystem_typeLarge unconnected -290.4 511.9 29.3 -0.6 0.6
## day -7.6 19.1 14.3 -0.4 0.7
## ecosystem_typeLarge unconnected:day 0.3 27.0 14.3 0.0 1.0
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.707
## day -0.937 0.662
## ecsystm_Lu: 0.662 -0.937 -0.707
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.5 0.116 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 969.3 983.9 -477.6 955.3 53
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.6 -0.1 0.5 2.6
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e+04 170
## day 1e+02 12 -1.00
## Residual 5e+05 688
## Number of obs: 60, groups: culture_ID, 10
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3625 271 34 13.4 6e-15 ***
## ecosystem_typeLarge unconnected -286 179 48 -1.6 0.1
## day -7 14 14 -0.5 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.331
## day -0.884 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Large connected to small"
## [1] "Large unconnected"
\(L_{S}\) vs \(L_{L}\)
ecosystem_type_i = c("Large connected to small",
"Large connected to large")Shannon
response_variable = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.4 0.271 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 35.2 55.2 -9.6 19.2 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.15 -0.67 -0.04 0.76 2.58
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.100
## day 3e-05 0.005 -1.00
## Residual 7e-02 0.267
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.224 0.144 15.394 8.5
## ecosystem_typeLarge connected to large 0.192 0.177 15.394 1.1
## day 0.007 0.007 16.266 1.0
## ecosystem_typeLarge connected to large:day -0.006 0.009 16.266 -0.6
## Pr(>|t|)
## (Intercept) 3e-07 ***
## ecosystem_typeLarge connected to large 0.3
## day 0.3
## ecosystem_typeLarge connected to large:day 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lctl day
## ecsyst_Lctl -0.816
## day -0.941 0.768
## ecsys_Lctl: 0.768 -0.941 -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.2 0.134 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 33.5 51.0 -9.8 19.5 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.02 -0.72 -0.09 0.77 2.59
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.111
## day 3e-05 0.006 -1.00
## Residual 7e-02 0.267
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1e+00 9e-02 2e+01 13.8
## ecosystem_typeLarge connected to large 9e-02 6e-02 7e+01 1.5
## day 4e-03 4e-03 2e+01 0.8
## Pr(>|t|)
## (Intercept) 2e-12 ***
## ecosystem_typeLarge connected to large 0.1
## day 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lctl
## ecsyst_Lctl -0.428
## day -0.852 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = 'optimx',
optCtrl = list(method = 'nlminb')))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.9 0.085 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 254.5 274.5 -119.3 238.5 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.35 -0.53 -0.07 0.52 3.04
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-01 0.61
## day 2e-04 0.02 -1.00
## Residual 7e-01 0.86
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 4.76 0.52 17.88 9.2
## ecosystem_typeLarge connected to large 1.03 0.64 17.88 1.6
## day -0.15 0.02 33.39 -6.1
## ecosystem_typeLarge connected to large:day -0.02 0.03 33.39 -0.7
## Pr(>|t|)
## (Intercept) 4e-08 ***
## ecosystem_typeLarge connected to large 0.1
## day 6e-07 ***
## ecosystem_typeLarge connected to large:day 0.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lctl day
## ecsyst_Lctl -0.816
## day -0.914 0.747
## ecsys_Lctl: 0.747 -0.914 -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -2.4 0.036 ** moderateClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb"))
##
## AIC BIC logLik deviance df.resid
## 253.1 270.6 -119.5 239.1 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.26 -0.57 -0.06 0.56 3.02
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 4e-01 0.63
## day 3e-04 0.02 -0.98
## Residual 7e-01 0.86
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.05 0.35 21.50 14
## ecosystem_typeLarge connected to large 0.59 0.26 15.00 2
## day -0.16 0.01 15.00 -12
## Pr(>|t|)
## (Intercept) 1e-12 ***
## ecosystem_typeLarge connected to large 0.04 *
## day 8e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lctl
## ecsyst_Lctl -0.492
## day -0.798 0.000Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.1 0.078 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 298.4 318.4 -141.2 282.4 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.27 -0.69 0.04 0.87 2.17
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-02 0.18
## day 9e-05 0.01 -1.00
## Residual 1e+00 1.16
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 6.17 0.60 16.52 10.2
## ecosystem_typeLarge connected to large 1.28 0.74 16.52 1.7
## day -0.02 0.03 15.54 -0.6
## ecosystem_typeLarge connected to large:day -0.04 0.04 15.54 -1.1
## Pr(>|t|)
## (Intercept) 1e-08 ***
## ecosystem_typeLarge connected to large 0.1
## day 0.6
## ecosystem_typeLarge connected to large:day 0.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lctl day
## ecsyst_Lctl -0.816
## day -0.936 0.764
## ecsys_Lctl: 0.764 -0.936 -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -2 0.046 ** moderateClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 297.6 315.1 -141.8 283.6 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.02 -0.71 0.05 0.82 2.22
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-01 0.41
## day 5e-04 0.02 -1.00
## Residual 1e+00 1.16
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 6.67 0.40 24.11 17
## ecosystem_typeLarge connected to large 0.53 0.26 75.30 2
## day -0.05 0.02 15.32 -2
## Pr(>|t|)
## (Intercept) 1e-14 ***
## ecosystem_typeLarge connected to large 0.04 *
## day 0.03 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lctl
## ecsyst_Lctl -0.433
## day -0.848 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 3.6 0.804 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -122.1 -102.1 69.1 -138.1 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7 -0.6 0.1 0.8 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 3e-17 5e-09 NaN
## Residual 1e-02 1e-01
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 7e-01 6e-02 9e+01 11.6
## ecosystem_typeLarge connected to large 2e-02 7e-02 9e+01 0.3
## day 6e-03 3e-03 9e+01 1.9
## ecosystem_typeLarge connected to large:day -3e-04 4e-03 9e+01 -0.1
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge connected to large 0.76
## day 0.07 .
## ecosystem_typeLarge connected to large:day 0.94
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lctl day
## ecsyst_Lctl -0.816
## day -0.935 0.763
## ecsys_Lctl: 0.763 -0.935 -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.6 0.512 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -124.1 -106.6 69.0 -138.1 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7 -0.6 0.1 0.8 1.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 3e-17 5e-09 NaN
## Residual 1e-02 1e-01
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 7e-01 4e-02 9e+01 18.1
## ecosystem_typeLarge connected to large 2e-02 3e-02 9e+01 0.7
## day 5e-03 2e-03 9e+01 3.1
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge connected to large 0.513
## day 0.002 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lctl
## ecsyst_Lctl -0.448
## day -0.836 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -7.5 0.003 *** strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1408.9 1428.9 -696.5 1392.9 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2 -0.5 -0.1 0.5 3.2
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-04 1e-02
## day 5e-07 7e-04 -1.00
## Residual 3e+05 6e+02
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3627 286 90 12.7
## ecosystem_typeLarge connected to large -735 350 90 -2.1
## day -8 15 90 -0.5
## ecosystem_typeLarge connected to large:day 56 18 90 3.1
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeLarge connected to large 0.038 *
## day 0.612
## ecosystem_typeLarge connected to large:day 0.003 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ec_Lctl day
## ecsyst_Lctl -0.816
## day -0.935 0.763
## ecsys_Lctl: 0.763 -0.935 -0.816
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.9 0.087 * weakClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1415.4 1432.9 -700.7 1401.4 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6 -0.6 0.0 0.4 3.2
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 8e+04 291
## day 3e+02 17 -1.00
## Residual 3e+05 571
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2969 204 29 14
## ecosystem_typeLarge connected to large 252 128 73 2
## day 30 10 15 3
## Pr(>|t|)
## (Intercept) 9e-15 ***
## ecosystem_typeLarge connected to large 0.053 .
## day 0.009 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) e_Lctl
## ecsyst_Lctl -0.418
## day -0.859 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Large connected to small"
## [1] "Large connected to large"
\(L_{L}\) vs \(L\)
ecosystem_type_i = c("Large connected to large",
"Large unconnected")Shannon
response_variable = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 3.8 0.887 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 21.2 41.2 -2.6 5.2 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.11 -0.72 -0.01 0.76 2.81
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.119
## day 5e-05 0.007 -1.00
## Residual 6e-02 0.245
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.416 0.097 18.467 14.6 1e-11
## ecosystem_typeLarge unconnected 0.065 0.168 18.467 0.4 0.7
## day 0.002 0.005 15.168 0.3 0.7
## ecosystem_typeLarge unconnected:day -0.002 0.009 15.168 -0.3 0.8
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.577
## day -0.945 0.546
## ecsystm_Lu: 0.546 -0.945 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.8 0.682 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 19.3 36.8 -2.7 5.3 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.13 -0.75 0.01 0.76 2.80
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-02 0.120
## day 5e-05 0.007 -1.00
## Residual 6e-02 0.245
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1e+00 8e-02 2e+01 17.6 9e-14 ***
## ecosystem_typeLarge unconnected 2e-02 5e-02 7e+01 0.4 0.7
## day 9e-04 4e-03 2e+01 0.2 0.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.225
## day -0.921 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2.1 0.396 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 265.4 285.4 -124.7 249.4 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9 -0.6 -0.1 0.5 2.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e-02 0.248
## day 1e-05 0.003 -1.00
## Residual 9e-01 0.950
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.79 0.35 31.23 16.3 <2e-16
## ecosystem_typeLarge unconnected 0.15 0.61 31.23 0.2 0.8
## day -0.17 0.02 68.52 -9.4 6e-14
## ecosystem_typeLarge unconnected:day 0.01 0.03 68.52 0.3 0.8
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day ***
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.577
## day -0.923 0.533
## ecsystm_Lu: 0.533 -0.923 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.2 0.185 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 263.5 281.0 -124.8 249.5 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9 -0.6 -0.1 0.5 2.8
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e-02 0.249
## day 1e-05 0.003 -1.00
## Residual 9e-01 0.950
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.73 0.30 33.41 19 <2e-16 ***
## ecosystem_typeLarge unconnected 0.32 0.24 15.08 1 0.2
## day -0.17 0.01 68.06 -11 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.263
## day -0.890 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -0.6 0.098 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 290.7 310.7 -137.4 274.7 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.02 -0.72 0.01 0.89 2.26
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 6e-13 8e-07 NaN
## Residual 1e+00 1e+00
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.45 0.41 90.00 18.4 <2e-16
## ecosystem_typeLarge unconnected -0.28 0.70 90.00 -0.4 0.692
## day -0.06 0.02 90.00 -2.9 0.005
## ecosystem_typeLarge unconnected:day 0.04 0.04 90.00 1.1 0.259
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day **
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.577
## day -0.935 0.540
## ecsystm_Lu: 0.540 -0.935 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.4 0.067 * weakClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 290.0 307.5 -138.0 276.0 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.05 -0.74 -0.09 0.77 2.27
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 2e-14 2e-07 NaN
## Residual 1e+00 1e+00
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.20 0.34 90.00 21 <2e-16 ***
## ecosystem_typeLarge unconnected 0.47 0.25 90.00 2 0.066 .
## day -0.05 0.02 90.00 -3 0.009 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.243
## day -0.907 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.3 0.255 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -136.1 -116.1 76.0 -152.1 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.7 0.1 0.8 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 2e-04 1e-02
## day 8e-07 9e-04 -1.00
## Residual 1e-02 1e-01
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.695 0.038 34.956 18 <2e-16
## ecosystem_typeLarge unconnected 0.063 0.066 34.956 1 0.35
## day 0.005 0.002 17.958 3 0.02
## ecosystem_typeLarge unconnected:day -0.005 0.003 17.958 -1 0.18
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day *
## ecosystem_typeLarge unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.577
## day -0.936 0.540
## ecsystm_Lu: 0.540 -0.936 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.1 0.345 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -136.2 -118.7 75.1 -150.2 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5 -0.6 0.1 0.8 1.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1e-03 0.037
## day 5e-06 0.002 -1.00
## Residual 1e-02 0.104
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.723 0.033 28.478 22 <2e-16 ***
## ecosystem_typeLarge unconnected -0.023 0.023 73.905 -1 0.34
## day 0.004 0.002 16.350 2 0.04 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.234
## day -0.914 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -13.9 < 0.001 **** very strongClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1416.8 1436.8 -700.4 1400.8 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.56 -0.07 0.56 2.36
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 7e+04 256
## day 3e+02 16 -1.00
## Residual 3e+05 569
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2892 222 23 13 4e-12
## ecosystem_typeLarge unconnected 445 385 23 1 0.26
## day 48 12 16 4 9e-04
## ecosystem_typeLarge unconnected:day -55 21 16 -3 0.02
##
## (Intercept) ***
## ecosystem_typeLarge unconnected
## day ***
## ecosystem_typeLarge unconnected:day *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu day
## ecsystm_tLu -0.577
## day -0.943 0.544
## ecsystm_Lu: 0.544 -0.943 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -10 0.001 *** strongClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1420.7 1438.2 -703.3 1406.7 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.54 -0.05 0.59 2.39
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e+05 503
## day 9e+02 30 -1.00
## Residual 3e+05 570
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3212 218 18 15 2e-11 ***
## ecosystem_typeLarge unconnected -516 129 66 -4 2e-04 ***
## day 30 12 15 2 0.02 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Lu
## ecsystm_tLu -0.197
## day -0.940 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Large connected to large"
## [1] "Large unconnected"
\(M_{M}\) vs \(M\)
ecosystem_type_i = c("Medium unconnected",
"Medium connected to medium")Shannon
response_variable = "shannon"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.7 0.193 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 52.7 72.7 -18.3 36.7 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.25 -0.63 -0.08 0.87 2.60
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-02 0.167
## day 6e-05 0.008 -1.00
## Residual 8e-02 0.291
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 1.418 0.118 15.033 12.0
## ecosystem_typeMedium unconnected -0.214 0.205 15.033 -1.0
## day -0.003 0.006 17.919 -0.5
## ecosystem_typeMedium unconnected:day 0.005 0.010 17.919 0.5
## Pr(>|t|)
## (Intercept) 4e-09 ***
## ecosystem_typeMedium unconnected 0.3
## day 0.7
## ecosystem_typeMedium unconnected:day 0.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu day
## ecsystm_tMu -0.577
## day -0.946 0.546
## ecsystm_Mu: 0.546 -0.946 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1 0.081 * weakClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 50.9 68.4 -18.5 36.9 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.21 -0.61 -0.05 0.84 2.58
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-02 0.172
## day 7e-05 0.008 -1.00
## Residual 8e-02 0.291
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.386 0.100 16.344 13.9 2e-10
## ecosystem_typeMedium unconnected -0.118 0.066 60.800 -1.8 0.08
## day -0.001 0.005 17.656 -0.2 0.84
##
## (Intercept) ***
## ecosystem_typeMedium unconnected .
## day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu
## ecsystm_tMu -0.221
## day -0.924 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Biomass
response_variable = "bioarea_mm2_per_ml"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 -1.6 0.062 * weakClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 217.6 237.6 -100.8 201.6 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.84 -0.75 -0.03 0.61 2.69
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 3e-01 0.59
## day 4e-04 0.02 -1.00
## Residual 5e-01 0.70
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.68 0.32 18.95 18 2e-13
## ecosystem_typeMedium unconnected -1.37 0.55 18.95 -2 0.02
## day -0.19 0.01 29.46 -13 1e-13
## ecosystem_typeMedium unconnected:day 0.05 0.03 29.46 2 0.04
##
## (Intercept) ***
## ecosystem_typeMedium unconnected *
## day ***
## ecosystem_typeMedium unconnected:day *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu day
## ecsystm_tMu -0.577
## day -0.934 0.539
## ecsystm_Mu: 0.539 -0.934 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.6 0.231 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 219.8 237.3 -102.9 205.8 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.77 -0.76 0.01 0.48 2.73
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 5e-01 0.73
## day 7e-04 0.03 -1.00
## Residual 5e-01 0.71
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.31 0.29 16.44 18 2e-12 ***
## ecosystem_typeMedium unconnected -0.27 0.19 23.37 -1 0.2
## day -0.17 0.01 20.93 -13 1e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu
## ecsystm_tMu -0.224
## day -0.922 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Richness
response_variable = "species_richness"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 2.5 0.479 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 322.5 342.5 -153.2 306.5 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.66 0.07 0.67 2.21
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1.146 1.07
## day 0.002 0.05 -0.98
## Residual 1.601 1.27
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 7.711 0.572 15.000 13.5
## ecosystem_typeMedium unconnected -0.216 0.990 15.000 -0.2
## day -0.098 0.028 15.000 -3.5
## ecosystem_typeMedium unconnected:day -0.009 0.049 15.000 -0.2
## Pr(>|t|)
## (Intercept) 9e-10 ***
## ecosystem_typeMedium unconnected 0.830
## day 0.003 **
## ecosystem_typeMedium unconnected:day 0.852
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu day
## ecsystm_tMu -0.577
## day -0.946 0.546
## ecsystm_Mu: 0.546 -0.946 -0.577Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.6 0.231 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 320.5 338.0 -153.3 306.5 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68 -0.65 0.09 0.67 2.22
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 1.153 1.07
## day 0.002 0.05 -0.98
## Residual 1.601 1.27
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.77 0.48 16.38 16 2e-11 ***
## ecosystem_typeMedium unconnected -0.39 0.32 15.00 -1 0.2
## day -0.10 0.02 15.00 -4 5e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu
## ecsystm_tMu -0.223
## day -0.922 0.000Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Evenness
response_variable = "evenness_pielou"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 0.1 0.144 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -130.3 -110.3 73.1 -146.3 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.30 -0.67 0.06 0.66 2.10
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 4e-17 6e-09 NaN
## Residual 1e-02 1e-01
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 0.682 0.039 90.000 18
## ecosystem_typeMedium unconnected -0.134 0.068 90.000 -2
## day 0.005 0.002 90.000 3
## ecosystem_typeMedium unconnected:day 0.006 0.004 90.000 2
## Pr(>|t|)
## (Intercept) <2e-16 ***
## ecosystem_typeMedium unconnected 0.050 *
## day 0.009 **
## ecosystem_typeMedium unconnected:day 0.070 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu day
## ecsystm_tMu -0.577
## day -0.935 0.540
## ecsystm_Mu: 0.540 -0.935 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.4 0.446 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -129.0 -111.5 71.5 -143.0 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4 -0.7 0.1 0.7 2.0
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 0e+00 0e+00
## day 2e-17 4e-09 NaN
## Residual 1e-02 1e-01
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.643 0.033 90.000 19.2 <2e-16
## ecosystem_typeMedium unconnected -0.019 0.024 90.000 -0.8 0.4
## day 0.008 0.002 90.000 4.5 2e-05
##
## (Intercept) ***
## ecosystem_typeMedium unconnected
## day ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu
## ecsystm_tMu -0.243
## day -0.907 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Median Size
response_variable = "median_body_area_µm2"We want to know whether the connection influenced this response variable. We first start from plotting how this response variable changed in connected and unconnected ecosystems throughout the experiment through its mean ± 95 confidence interval:
plot.ecosystems.points(ds_ecosystems,
ecosystem_type_i,
response_variable)
Following the initial inspection, we proceed to analyse differences among ecosystems. Our first step involves filtering the data to isolate the relevant data for analysis. Specifically, we exclude data points where the response variable couldn’t be computed, as well as time points preceding the initial disturbance and resource flow. Then we plot the data to make sure that what filtered the data in the right way.
filtered_data = ds_ecosystems %>%
filter(time_point >= first_time_point_model,
time_point <= last_time_point_model,
ecosystem_type %in% ecosystem_type_i,
!is.na(!!sym(response_variable)))plot.ecosystems.points(filtered_data,
ecosystem_type_i,
response_variable) 
Then, given that we have gathered measurements from the same
ecosystem on multiple occasions, we can develop mixed effect models to
examine how the connection influenced this variable. To study the
effects of ecosystem connection we compare two models to a null model
using ANOVA: a full model and a reduced model. In all models, we treat
culture ID as having a random effect on how the slope and intercept of
the relationship between response variable and time, with the slope and
intercept being correlated (Bates et al.
2015). The full model contains the interaction of connection with
time
(Response variable ~ connection * day + (day | culture ID)),
the reduced model contains the connection but without the interaction
with time
(Response variable ~ connection + day + (day | culture ID)),
and the null model doesn’t contain the connection at all
(Response variable ~ day + (day | culture ID)). If any of
the two model comparisons is significant, then ecosystem connection had
an effect.
full_model = lmer(
get(response_variable) ~
ecosystem_type * day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
reduced_model = lmer(
get(response_variable) ~
ecosystem_type + day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))
null_model = lmer(
get(response_variable) ~
day +
(day | culture_ID),
data = filtered_data,
REML = FALSE,
control = lmerControl(optimizer = "Nelder_Mead"))Full model vs null model
Click to view the results of the ANOVA comparison between full and null model.
model_stats_full = compute.model.stats(full_model,
null_model,
"mixed_model")
model_stats_full %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 3.7 0.862 noneClick to view the full model output
print(summary(full_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type * day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1446.3 1466.3 -715.2 1430.3 82
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6 -0.4 0.1 0.5 3.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e+05 782
## day 3e+03 54 -1.00
## Residual 4e+05 611
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3405 332 16 10.2 2e-08
## ecosystem_typeMedium unconnected -89 576 16 -0.2 0.9
## day 14 21 15 0.7 0.5
## ecosystem_typeMedium unconnected:day 10 36 15 0.3 0.8
##
## (Intercept) ***
## ecosystem_typeMedium unconnected
## day
## ecosystem_typeMedium unconnected:day
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu day
## ecsystm_tMu -0.577
## day -0.966 0.558
## ecsystm_Mu: 0.558 -0.966 -0.577
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the full model residual plots
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(full_model),
residuals = resid(full_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(full_model))
Reduced vs null model
Click to view the results of the ANOVA comparison between reduced and null model.
model_stats_reduced = compute.model.stats(reduced_model,
null_model,
"mixed_model")
model_stats_reduced %>%
mutate(deltaAIC = round(deltaAIC, digits = 1),
p_value = round(p_value, digits = 3),
R2 = NULL,
evidence = "",
evidence = ifelse(p_value > 0.1,
"none",
evidence),
evidence = ifelse(p_value < 0.1,
"* weak",
evidence),
evidence = ifelse(p_value < 0.05,
"** moderate",
evidence),
evidence = ifelse(p_value < 0.01,
"*** strong",
evidence),
evidence = ifelse(p_value < 0.001,
"**** very strong",
evidence),
p_value = ifelse(p_value < 0.001,
"< 0.001",
p_value)) %>%
print()## deltaAIC p_value evidence
## 1 1.8 0.642 noneClick to view the reduced model output
print(summary(reduced_model), digits = 1)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: get(response_variable) ~ ecosystem_type + day + (day | culture_ID)
## Data: filtered_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 1444.4 1461.9 -715.2 1430.4 83
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6 -0.5 0.1 0.5 3.9
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## culture_ID (Intercept) 6e+05 785
## day 3e+03 55 -1.00
## Residual 4e+05 611
## Number of obs: 90, groups: culture_ID, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3352 277 17 12.1 8e-10 ***
## ecosystem_typeMedium unconnected 70 149 49 0.5 0.6
## day 17 17 15 1.0 0.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ecs_Mu
## ecsystm_tMu -0.180
## day -0.950 0.000
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')Click to view the reduced model residual plots
#Create resid vs fitted
res_vs_fit = filtered_data %>%
mutate(predicted = fitted(reduced_model),
residuals = resid(reduced_model)) %>%
plot_ly(x = ~predicted,
y = ~residuals,
type = "scatter",
mode = "markers",
marker = list(size = 5, color = "#4C78A8"),
text = paste(" ID: ",
filtered_data$culture_ID,
"<br>",
"Day: ",
filtered_data$day,
"<br>",
"Patch Type: ",
filtered_data$ecosystem_type,
"<br>",
"Biomass density: ",
round(filtered_data$bioarea_mm2_per_ml, digits = 2),
"<br>",
"Species richness: ",
filtered_data$species_richness,
"<br>"),
hoverinfo = "text") %>%
plotly::layout(title = "Residuals vs. Fitted Values",
xaxis = list(title = "Fitted Values"),
yaxis = list(title = "Residuals"))res_vs_fitqqnorm(resid(reduced_model))
Populations
for(ecosystem_type_i in ecosystem_type_i){
print(ecosystem_type_i)
p = ds_ecosystems %>%
filter(ecosystem_type == ecosystem_type_i) %>%
group_by(day) %>%
summarise(
Ble = mean(Ble_indiv_per_ml_dominance, na.rm = TRUE),
# Ble_se = sd(Ble_indiv_per_ml_dominance, na.rm = TRUE) / sqrt(n()),
# Ble_ci = qt(c(0.025, 0.975), df = n() - 1) * Ble_se,
Cep = mean(Cep_indiv_per_ml_dominance, na.rm = TRUE),
Col = mean(Col_indiv_per_ml_dominance, na.rm = TRUE),
Eug = mean(Eug_indiv_per_ml_dominance, na.rm = TRUE),
Eup = mean(Eup_indiv_per_ml_dominance, na.rm = TRUE),
Lox = mean(Lox_indiv_per_ml_dominance, na.rm = TRUE),
Pau = mean(Pau_indiv_per_ml_dominance, na.rm = TRUE),
Pca = mean(Pca_indiv_per_ml_dominance, na.rm = TRUE),
Spi = mean(Spi_indiv_per_ml_dominance, na.rm = TRUE),
Spi_te = mean(Spi_te_indiv_per_ml_dominance, na.rm = TRUE),
Tet = mean(Tet_indiv_per_ml_dominance, na.rm = TRUE)
) %>%
pivot_longer(Ble:Tet, names_to = "species", values_to = "species_indiv_per_ml") %>%
ggplot(aes(
x = day,
y = species_indiv_per_ml,
group = interaction(day, species),
color = species
)) +
geom_point(position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(
aes(group = species),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
labs(x = axis_names %>%
filter(variable == "day") %>%
pull(axis_name),
y = axis_names %>%
filter(variable == "dominance") %>%
pull(axis_name)) +
coord_cartesian(ylim = c(0, 100))
print(p)
}## [1] "Medium unconnected"
## [1] "Medium connected to medium"
Results
Meta-ecosystem diversity & function
We want here to plot the final paper version of the biodiversity and productivity of meta-ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to change the size of the plot.
# Define meta-ecosystems you want to plot.
metaecosystem_type_i = c("Medium-Medium meta-ecosystem",
"Medium-Medium unconnected",
"Small-Large meta-ecosystem",
"Small-Large unconnected")# Write function to plot a response variable. Afterwards you can use this function to plot alpha, beta, gamma diversity, and biomass.
plot.single.plot = function(response_variable){
ds_metaecosystems %>%
filter(metaecosystem_type %in% metaecosystem_type_i,
!is.na(!!sym(response_variable))) %>%
summarySE(measurevar = response_variable,
groupvars = c("day", "metaecosystem_type", "type", "connection")) %>%
ggplot(aes(x = day,
y = get(response_variable),
group = interaction(day, metaecosystem_type),
color = type,
linetype = connection)) +
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(stat = "summary",
fun = "mean",
aes(group = metaecosystem_type),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
geom_errorbar(aes(ymax = get(response_variable) + ci,
ymin = get(response_variable) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable],
color = "") +
scale_color_manual(values = c("#762a83",
"#1b7837")) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm")) +
guides(color = guide_legend(title = NULL,
nrow = 2),
linetype = guide_legend(title = NULL,
nrow = 2)) +
theme(plot.margin = unit(c(ggarrange_margin_left,
ggarrange_margin_right,
ggarrange_margin_bottom,
ggarrange_margin_left),
"cm")) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color)
}# Combine plots of alpha, beta, gamma biodiversity and biomass.
p_combined = ggarrange(plot.single.plot("mean_shannon") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text", size = paper_labels_size) +
font("ylab", size = paper_labels_size),
plot.single.plot("bray_curtis") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("metaecosystem_richness") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("total_metaecosystem_bioarea_mm2") +
font("legend.text",
size = paper_labels_size) +
font("xlab",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size) +
scale_x_continuous(breaks = unique(ds_metaecosystems$day)),
heights = c(0.8, 0.8, 0.8, 1),
nrow = 4,
common.legend = TRUE,
align = "v",
labels = c("(a)", "(b)", "(c)", "(d)"),
label.x = 0.1,
label.y = 0.8) %>%
print()
Ecosystem diversity & function
We want here to plot the final paper version of the biodiversity and productivity of the small and large ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have the underscores in the legend. We don’t use underscores in the analysis because we can’t easily input them from a level name vector.
# Define ecosystems you want to plot.
ecosystem_type_input = c("Small connected to large",
"Small connected to small",
"Small unconnected",
"Large connected to small",
"Large connected to large",
"Large unconnected")# Construct function to plot how the response variable (biomass or Shannon) of small and large ecosystems changes across time.
plot.single.plot = function(response_variable){
ds_ecosystems %>%
filter(ecosystem_type %in% ecosystem_type_input,
!is.na(!!sym(response_variable))) %>%
summarySE(measurevar = response_variable,
groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
ggplot(aes(x = day,
y = get(response_variable),
group = interaction(day, ecosystem_type),
color = ecosystem_type,
linetype = ecosystem_type)) +
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(stat = "summary",
fun = "mean",
aes(group = ecosystem_type),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
geom_errorbar(aes(ymax = get(response_variable) + ci,
ymin = get(response_variable) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable],
color = "") +
scale_color_manual(values = c("#993404",
"#993404",
"#993404",
"#3182bd",
"#3182bd",
"#3182bd"),
label = expression(S[L],
S[S],
S,
L[S],
L[L],
L)) +
scale_linetype_manual(values = c("solid",
"dashed",
"dotted",
"solid",
"dashed",
"dotted"),
label = expression(S[L],
S[S],
S,
L[S],
L[L],
L)) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width) +
geom_hline(yintercept = 0,
color = zero_line_colour,
linetype = zero_line_line_type,
linewidth = zero_line_line_width) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm")) +
guides(color = guide_legend(title = NULL,
nrow = 3),
linetype = guide_legend(title = NULL,
nrow = 3)) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color)
}# Combine plots
p_combined = ggarrange(plot.single.plot("shannon") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("bioarea_mm2_per_ml") +
font("legend.text",
size = paper_labels_size) +
font("xlab",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size) +
scale_x_continuous(breaks = unique(ds_ecosystems$day)),
heights = c(0.8, 0.8, 1),
nrow = 2,
align = "v",
labels = c("(a)", "(b)"),
label.x = 0.1,
label.y = 0.8,
common.legend = TRUE) %>%
print()## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs produced
We want here to plot the final paper version of the biodiversity and productivity of the medium ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have the underscores in the legend. We don’t use underscores in the analysis because we can’t easily input them from a level name vector.
# Define ecosystems you want to plot.
ecosystem_type_input = c("Medium connected to medium",
"Medium unconnected")# Construct function to plot how the response variable (biomass or Shannon) of small and large ecosystems changes across time.
plot.single.plot = function(response_variable){
ds_ecosystems %>%
filter(ecosystem_type %in% ecosystem_type_input,
!is.na(!!sym(response_variable))) %>%
summarySE(measurevar = response_variable,
groupvars = c("day", "time_point", "ecosystem_type", "ecosystem_size", "connection")) %>%
ggplot(aes(x = day,
y = get(response_variable),
group = interaction(day, ecosystem_type),
color = ecosystem_type,
linetype = ecosystem_type)) +
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_line(stat = "summary",
fun = "mean",
aes(group = ecosystem_type),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
geom_errorbar(aes(ymax = get(response_variable) + ci,
ymin = get(response_variable) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable],
color = "") +
scale_color_manual(values = c("#d95f0e",
"#d95f0e"),
label = expression(M[M],
M)) +
scale_linetype_manual(values = c("dashed",
"dotted"),
label = expression(M[M],
M)) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width) +
geom_hline(yintercept = 0,
color = zero_line_colour,
linetype = zero_line_line_type,
linewidth = zero_line_line_width) +
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm")) +
guides(color = guide_legend(title = NULL,
nrow = 3),
linetype = guide_legend(title = NULL,
nrow = 3)) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color)
}# Combine plots
p_combined = ggarrange(plot.single.plot("shannon") +
rremove("xlab") +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
font("legend.text",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size),
plot.single.plot("bioarea_mm2_per_ml") +
font("legend.text",
size = paper_labels_size) +
font("xlab",
size = paper_labels_size) +
font("ylab",
size = paper_labels_size) +
scale_x_continuous(breaks = unique(ds_ecosystems$day)),
heights = c(0.8, 0.8, 1),
nrow = 2,
align = "v",
labels = c("(a)", "(b)"),
label.x = 0.1,
label.y = 0.8,
common.legend = TRUE) %>%
print()
Ecosystem autotrophic/heterotrophic ratio
We want here to plot the final paper version of the ratio between autotrophic and heterotrophic biomass in small, medium, and large unconnected ecosystems. We need to plot it again instead of using the plots we used in the analysis because we want to have S, M, and L in the legend.
# Define ecosystems and response variable you want to plot.
ecosystem_type_input = c("S",
"M",
"L")
response_variable = "auto_hetero_ratio"# Construct plot
p = ds_ecosystems %>%
# Manipulate
mutate(ecosystem_type = case_when(ecosystem_type == "Small unconnected" ~ "S",
ecosystem_type == "Medium unconnected" ~ "M",
ecosystem_type == "Large unconnected" ~ "L")) %>%
filter(ecosystem_type %in% ecosystem_type_input,
!is.na(!!sym(response_variable))) %>%
summarySE(measurevar = response_variable,
groupvars = c("day", "ecosystem_type", "ecosystem_size", "connection")) %>%
# Create plot
ggplot(aes(x = day,
y = get(response_variable),
group = interaction(day, ecosystem_type),
color = ecosystem_type)) +
# Points
geom_point(stat = "summary",
fun = "mean",
position = position_dodge(dodging),
size = treatment_points_size) +
geom_errorbar(aes(ymax = get(response_variable) + ci,
ymin = get(response_variable) - ci),
width = width_errorbar,
position = position_dodge(dodging)) +
# Lines
geom_line(stat = "summary",
fun = "mean",
aes(group = ecosystem_type),
position = position_dodge(dodging),
linewidth = treatment_lines_linewidth) +
# Axes and legend
labs(x = axis_names$axis_name[axis_names$variable == "day"],
y = axis_names$axis_name[axis_names$variable == response_variable],
color = "") +
scale_x_continuous(breaks = unique(ds_ecosystems$day)) +
guides(color = guide_legend(title = NULL,
nrow = 1),
linetype = guide_legend(title = NULL,
nrow = 1)) +
scale_color_manual(values = c("#000000",
"#737373",
"#bdbdbd")) +
# Extra graphic elements
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.position = legend_position,
legend.key.width = unit(legend_width_cm, "cm"),
axis.title.x = element_text(size = paper_labels_size),
axis.title.y = element_text(size = paper_labels_size),
legend.text = element_text(size = paper_labels_size)) +
geom_rect(xmin = grey_background_xmin,
xmax = grey_background_xmax,
ymin = grey_background_ymin,
ymax = grey_background_ymax,
fill = grey_background_fill,
alpha = grey_background_alpha,
color = grey_background_color) +
geom_hline(yintercept = 0,
color = zero_line_colour,
linetype = zero_line_line_type,
linewidth = zero_line_line_width) +
geom_vline(xintercept = resource_flow_days,
linetype = resource_flow_line_type,
color = resource_flow_line_colour,
linewidth = resource_flow_line_width)## Warning in qt(conf.interval/2 + 0.5, datac$N - 1): NaNs producedp
Evaporation
During the experiment we noticed that microwaving ecosystem sub-samples for three minutes to create disturbance caused the evaporation of the ecosystems. However, we don’t know exactly how much evaporated and how much we should refill the ecosystems to bring them back to the original volume. Therefore, here I quantify the evaporation of 5.75 and 6.75 ml of deionised water, which represent low and high disturbance, respectively. For each disturbance level, I microwaved 15 tubes of that disturbance level for three minutes and measured their evaporation. To do so, I weighed the water before the microwaving (weigh tubes, add water, reweigh tubes) and after it (weigh Becker, pour water into it, reweigh Becker).
evaporation.test = read.csv(here("1_experiment", "evaporation_test","evaporation_test_initial.csv"), header = TRUE)
evaporation.test %>%
ggplot(aes (x = as.character(water_pipetted),
y = weight_water_evaporated,
group = interaction(water_pipetted, as.character(rack)),
fill = as.character(rack))) +
geom_boxplot(width = boxplot_width) +
labs(x = "Water volume (ml)" ,
y = "Evaporation (g)",
fill = "Rack replicate")
Furthermore, during the experiment we noticed that microwaving five 6.75 ml ecosystems sub-samples with ten empty tubes for three minutes to create disturbance caused the evaporation of the sub-samples more than if they were with other sub-samples. However, we don’t know exactly how much evaporated and how much we should refill the ecosystems to bring them back to the original volume. Therefore, here I quantify the evaporation of five 6.75 ml sub-samples with ten empty or filled falcon tubes. The weighting was conducted as above.
evaporation.test = read.csv(here("1_experiment", "evaporation_test", "evaporation_test_fill_nofill.csv"), header = TRUE)
evaporation.test %>%
ggplot(aes (x = all_tubes_water,
y = weight_water_evaporated)) +
geom_boxplot(width = boxplot_width) +
labs(x = "Water in the other 10 tubes" ,
y = "Evaporation (g)")
Analysis scripts
Video analysis
To analyse the videos I took of the ecosystems, I used the package BEMOVI. For this, I had to use the powerful computer. Below is the code utilised for video analysis on the powerful computer.
# Clear workspace
rm(list = ls())
# Set working directory
setwd("/media/mendel-himself/ID_061_Ema2/PatchSizePilot/training")
# Load required libraries
# library(devtools)
# install_github("femoerman/bemovi", ref="master")
library(bemovi)
library(parallel)
library(doParallel)
library(foreach)
# Define memory allocation parameters (in MB)
memory.alloc <- 240000 # Total memory allocated
memory.per.identifier <- 40000 # Memory per identifier
memory.per.linker <- 5000 # Memory per linker
memory.per.overlay <- 60000 # Memory per overlay
# Set paths for tools and particle linker
tools.path <- "/home/mendel-himself/bemovi_tools/" # Path to tools folder
to.particlelinker <- tools.path
# Set directories and file names
to.data <- paste(getwd(), "/", sep = "")
video.description.folder <- "0_video_description/"
video.description.file <- "video_description.txt"
raw.video.folder <- "1_raw/"
raw.avi.folder <- "1a_raw_avi/"
metadata.folder <- "1b_raw_meta/"
particle.data.folder <- "2_particle_data/"
trajectory.data.folder <- "3_trajectory_data/"
temp.overlay.folder <- "4a_temp_overlays/"
overlay.folder <- "4_overlays/"
merged.data.folder <- "5_merged_data/"
ijmacs.folder <- "ijmacs/"
######################################################################
# VIDEO PARAMETERS
# Define video parameters
fps <- 25 # Video frame rate (frames per second)
total_frames <- 125 # Total length of video (frames)
width <- 2048 # Video width (pixels)
height <- 2048 # Video height (pixels)
measured_volume <- 34.4 # Measured volume (microliters) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
pixel_to_scale <- 4.05 # Size of a pixel (micrometers) for Leica M205 C with 1.6 fold magnification, sample height 0.5 mm and Hamamatsu Orca Flash 4
video.format <- "cxd" # Video file format (avi, cxd, mov, tiff)
difference.lag <- 10 # Difference lag
thresholds <- c(13, 255) # Threshold values of pixel intensity (considered a measure of pixel "whiteness") for determining if a pixel belongs to an individual rather than the background
######################################################################
# FILTERING PARAMETERS
# optimized for Perfex Pro 10 stereomicrocope with Perfex SC38800 (IDS UI-3880LE-M-GL) camera
# tested stereomicroscopes: Perfex Pro 10, Nikon SMZ1500, Leica M205 C
# tested cameras: Perfex SC38800, Canon 5D Mark III, Hamamatsu Orca Flash 4
# tested species: Tet, Col, Pau, Pca, Eug, Chi, Ble, Ceph, Lox, Spi
particle_min_size <- 10 # Minimum particle size (pixels)
particle_max_size <- 1000 # Maximum particle size (pixels)
trajectory_link_range <- 3 # Number of adjacent frames for linking particles
trajectory_displacement <- 16 # Maximum displacement of a particle between frames
# Filtering criteria
filter_min_net_disp <- 25 # Minimum net displacement (µm)
filter_min_duration <- 1 # Minimum duration (s)
filter_detection_freq <- 0.1 # Minimum detection frequency (1/s)
filter_median_step_length <- 3 # Minimum median step length (µm)
######################################################################
# VIDEO ANALYSIS
# Check if all tools are installed and set permissions
check_tools_folder(tools.path)
system(paste0("chmod a+x ", tools.path, "bftools/bf.sh"))
system(paste0("chmod a+x ", tools.path, "bftools/bfconvert"))
system(paste0("chmod a+x ", tools.path, "bftools/showinf"))
# Convert video files to compressed avi format
convert_to_avi(to.data,
raw.video.folder,
raw.avi.folder,
metadata.folder,
tools.path,
fps,
video.format)
# Uncomment the following lines for testing
# check_video_file_names(to.data, raw.avi.folder, video.description.folder, video.description.file)
# check_threshold_values(to.data, raw.avi.folder, ijmacs.folder, 2, difference.lag, thresholds, tools.path, memory.alloc)
# Identify particles in the video
locate_and_measure_particles(to.data,
raw.avi.folder,
particle.data.folder,
difference.lag,
min_size = particle_min_size,
max_size = particle_max_size,
thresholds = thresholds,
tools.path,
memory = memory.alloc,
memory.per.identifier = memory.per.identifier,
max.cores = detectCores() - 1)
# Link particles across frames to form trajectories
link_particles(to.data,
particle.data.folder,
trajectory.data.folder,
linkrange = trajectory_link_range,
disp = trajectory_displacement,
start_vid = 1,
memory = memory.alloc,
memory_per_linkerProcess = memory.per.linker,
raw.avi.folder,
max.cores = detectCores() - 1,
max_time = 1)
# Merge video description file with particle data
merge_data(to.data,
particle.data.folder,
trajectory.data.folder,
video.description.folder,
video.description.file,
merged.data.folder)
# Load the merged data
load(paste0(to.data, merged.data.folder, "Master.RData"))
# Filter trajectory data based on defined criteria
trajectory.data.filtered <- filter_data(trajectory.data,
filter_min_net_disp,
filter_min_duration,
filter_detection_freq,
filter_median_step_length)
# Summarize trajectory data to individual-based data
morph_mvt <- summarize_trajectories(trajectory.data.filtered,
calculate.median = F,
write = T,
to.data,
merged.data.folder)
# Summarize sample level data
summarize_populations(trajectory.data.filtered,
morph_mvt,
write = T,
to.data,
merged.data.folder,
video.description.folder,
video.description.file,
total_frames)
# Create overlays for validation
create.subtitle.overlays(to.data,
traj.data = trajectory.data.filtered,
raw.video.folder,
raw.avi.folder,
temp.overlay.folder,
overlay.folder,
fps,
vid.length = total_frames / fps,
width,
height,
tools.path = tools.path,
overlay.type = "number",
video.format)
# Create overlays (old method)
create_overlays(traj.data = trajectory.data.filtered,
to.data = to.data,
merged.data.folder = merged.data.folder,
raw.video.folder = raw.avi.folder,
temp.overlay.folder = "4a_temp_overlays_old/",
overlay.folder = "4_overlays_old/",
width = width,
height = height,
difference.lag = difference.lag,
type = "traj",
predict_spec = F,
contrast.enhancement = 1,
IJ.path = "/home/mendel-himself/bemovi_tools",
memory = memory.alloc,
max.cores = detectCores() - 1,
memory.per.overlay = memory.per.overlay)Species identification
To avoid transferring all the data from the powerful computer, I performed species identification on that system and subsequently imported the results into the Rstudio folder on my personal computer. Below is the code utilised for species identification on the powerful computer.
# Clear the workspace
rm(list = ls())
# Uncomment and install required packages if not already installed
#install.packages("e1071",dependencies = T)
#install.packages("devtools",dependencies = T)
#install_github("pennekampster/bemovi", ref="master")
#library(devtools)
# Load required libraries
library(bemovi)
library(e1071)
library("here")
library("tidyverse")
# Define time points in the experiment
time_points_in_experiment = c("t0", "t1", "t2", "t3", "t4", "t5", "t6", "t7")
# Loop through each time point in the experiment
for (time_point in time_points_in_experiment) {
# Define folder names and paths
video.description.folder = "0_video_description/"
video.description.file = "video_description.txt"
merged.data.folder = "5_merged_data/"
monocultures_folder_path = here("biomass_analysis", "training", "")
mixed_cultures_folder_path = here("biomass_analysis", time_point, "")
#Parameters used in the video analysis script
fps = 25
nsv = 5
measured_volume = 34.4
pixel_to_scale = 4.05
filter_min_net_disp = 25
filter_min_duration = 1
filter_detection_freq = 0.1
filter_median_step_length = 3
# Load master dataset of mono-cultures
load(paste0(monocultures_folder_path, merged.data.folder, "Master.RData"))
trajectory.data_monocultures = trajectory.data
rm(trajectory.data)
# Filter the master data of mono-cultures using the same parameters as in the video analysis script
trajectory.data_monocultures.filtered = filter_data(trajectory.data_monocultures,
filter_min_net_disp,
filter_min_duration,
filter_detection_freq,
filter_median_step_length)
# Summarize trajectory data to individual-based data
morph_mvt = summarize_trajectories(data = trajectory.data_monocultures.filtered,
calculate.median = FALSE,
write = TRUE,
to.data = monocultures_folder_path,
merged.data.folder = merged.data.folder) %>%
mutate(comment = NULL)
# Prepare training data by removing incomplete cases
training_data = morph_mvt[complete.cases(morph_mvt), ]
# Train SVM model on the training data
svm1 = svm(
factor(species) ~
mean_grey +
sd_grey +
mean_area +
sd_area +
mean_perimeter +
mean_turning +
sd_turning +
sd_perimeter +
mean_major +
sd_major +
mean_minor +
sd_minor +
mean_ar +
sd_ar +
duration +
max_net +
net_disp +
net_speed +
gross_disp +
max_step +
min_step +
sd_step +
sd_gross_speed +
max_gross_speed +
min_gross_speed ,
data = training_data,
probability = T,
na.action = na.pass)
# Generate and print confusion matrix
confusion.matrix = table(svm1$fitted, training_data$species)
confusion.matrix.nd = confusion.matrix
diag(confusion.matrix.nd) = 0
svm1$confusion = cbind(confusion.matrix,
class.error = rowSums(confusion.matrix.nd) / rowSums(confusion.matrix))
print(paste("Confusion matrix of time point", time_point))
print(svm1$confusion)
# Extract unique species names
species.names = unique(trajectory.data_monocultures$species)
# Load mixed cultures dataset
load(paste0(mixed_cultures_folder_path, merged.data.folder, "Master.RData"))
trajectory.data_mixed = trajectory.data
rm(trajectory.data)
# Filter mixed cultures data using the same parameters
trajectory.data_mixed.filtered = filter_data(trajectory.data_mixed,
filter_min_net_disp,
filter_min_duration,
filter_detection_freq,
filter_median_step_length)
# Summarize trajectory data to individual-based data
morph_mvt = summarize_trajectories(data = trajectory.data_mixed.filtered,
calculate.median = FALSE,
write = TRUE,
to.data = mixed_cultures_folder_path,
merged.data.folder = merged.data.folder)[, which(colnames(morph_mvt) != "Col_manual")] %>%
mutate(comment = NULL)
# Prepare data for prediction by removing incomplete cases
data.to.predict = morph_mvt[complete.cases(morph_mvt),]
# Predict species using the trained SVM model
p.id = predict(object = svm1, data.to.predict, type = "response")
data.to.predict$predicted_species = as.character(p.id)
# Summarize population data
pop.data = summarize_populations(traj.data = trajectory.data_monocultures.filtered,
sum.data = morph_mvt,
write = TRUE,
to.data = mixed_cultures_folder_path,
merged.data.folder = merged.data.folder,
video.description.folder = video.description.folder,
video.description.file = video.description.file,
total_frame = fps * nsv)
# Function to calculate species density
species.density = function(sample_output,
indiv_predicted,
species_names,
total_frames,
mv = measured_volume) {
samples = unique(indiv_predicted$file)
sp.dens = matrix(0,
nrow(sample_output),
length(species_names))
colnames(sp.dens) = species_names
for (i in 1:length(samples)) {
indiv = subset(indiv_predicted, file == samples[i])
spec = unique(indiv$predicted_species)
for (j in 1:length(spec)) {
all.indiv.sp = subset(indiv,
predicted_species == spec[j])
dens = sum(all.indiv.sp$N_frames) / total_frames / mv
sp.dens[which(sample_output$file == as.character(samples[i])), which(species_names == spec[j])] = dens
}
}
return(cbind(sample_output, sp.dens))
}
# Calculate species density for the current time point
output = species.density(pop.data,
data.to.predict,
species.names,
total_frames = fps * nsv,
mv = measured_volume)
# Save the species density results to a CSV file
file_name = paste0("species_ID_", time_point, ".csv")
write.csv(output, here("biomass_analysis", "species_ID_results", file_name))
rm(output)
}Other
Running time
## Time difference of 1.8 minsDisturbance input
Check that disturbance_global_input is what you set:
print(paste0("Disturbance = ", disturbance_global_input))## [1] "Disturbance = high"Useful code
If you want to change a certain part of the code using the following code in Unix:
#Rmd script
cd /Users/Ema/Documents/Github/PatchSize/3_r_files
sed -i '' 's/old_string/new_string/g' *.Rmd
#R script
cd /Users/ema/Documents/GitHub/PatchSize/3_r_files/functions
sed -i '' 's/old_string/new_string/g' *.Ryou want to share a dataset and get a reproducible object, use the following R code:
dput()Crashed cultures
The only type of ecosystem where all cultures crashed was small connected to small at high disturbance.
R version
R.version.string## [1] "R version 4.3.2 (2023-10-31)"R package versions
The R packages we used with their version are as follows:
sessionInfo()## R version 4.3.2 (2023-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Sonoma 14.2.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: Europe/Zurich
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices datasets utils methods base
##
## other attached packages:
## [1] conflicted_1.2.0 combinat_0.0-8 Rmisc_1.5.1 betapart_1.6
## [5] vegan_2.6-6.1 lattice_0.22-6 permute_0.9-7 lmerTest_3.1-3
## [9] lme4_1.1-35.4 Matrix_1.6-5 plotly_4.10.4 ggpubr_0.6.0
## [13] lubridate_1.9.3 forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
## [17] purrr_1.0.2 readr_2.1.5 tidyr_1.3.1 tibble_3.2.1
## [21] ggplot2_3.5.1 tidyverse_2.0.0 plyr_1.8.9 renv_1.0.7.9000
## [25] testthat_3.2.1.1 here_1.0.1
##
## loaded via a namespace (and not attached):
## [1] gridExtra_2.3 rlang_1.1.4 magrittr_2.0.3
## [4] compiler_4.3.2 mgcv_1.9-0 vctrs_0.6.5
## [7] pkgconfig_2.0.3 fastmap_1.2.0 backports_1.5.0
## [10] labeling_0.4.3 magic_1.6-1 utf8_1.2.4
## [13] rmarkdown_2.27 pracma_2.4.4 tzdb_0.4.0
## [16] nloptr_2.1.1 itertools_0.1-3 waldo_0.5.2
## [19] xfun_0.45 cachem_1.1.0 jsonlite_1.8.8
## [22] highr_0.11 broom_1.0.6 parallel_4.3.2
## [25] cluster_2.1.4 R6_2.5.1 bslib_0.7.0
## [28] stringi_1.8.4 pkgload_1.3.4 car_3.1-2
## [31] boot_1.3-30 brio_1.1.5 jquerylib_0.1.4
## [34] rcdd_1.6 numDeriv_2016.8-1.1 Rcpp_1.0.12
## [37] iterators_1.0.14 knitr_1.47 snow_0.4-4
## [40] picante_1.8.2 splines_4.3.2 timechange_0.3.0
## [43] tidyselect_1.2.1 rstudioapi_0.16.0 abind_1.4-5
## [46] yaml_2.3.8 codetools_0.2-20 minpack.lm_1.2-4
## [49] withr_3.0.0 evaluate_0.24.0 desc_1.4.3
## [52] pillar_1.9.0 carData_3.0-5 foreach_1.5.2
## [55] geometry_0.4.7 generics_0.1.3 rprojroot_2.0.4
## [58] hms_1.1.3 munsell_0.5.1 scales_1.3.0
## [61] minqa_1.2.7 glue_1.7.0 lazyeval_0.2.2
## [64] tools_4.3.2 data.table_1.15.4 ggsignif_0.6.4
## [67] cowplot_1.1.3 fastmatch_1.1-4 grid_4.3.2
## [70] ape_5.8 crosstalk_1.2.1 colorspace_2.1-0
## [73] nlme_3.1-163 cli_3.6.3 optimx_2023-10.21
## [76] fansi_1.0.6 viridisLite_0.4.2 doSNOW_1.0.20
## [79] gtable_0.3.5 rstatix_0.7.2 sass_0.4.9
## [82] digest_0.6.36 farver_2.1.2 htmlwidgets_1.6.4
## [85] memoise_2.0.1 htmltools_0.5.8.1 lifecycle_1.0.4
## [88] httr_1.4.7 MASS_7.3-60References
Bates, Douglas, Martin Mächler, Benjamin M. Bolker, and Steven C.
Walker. 2015. “Fitting Linear Mixed-Effects Models Using
Lme4.” Journal of Statistical Software 67. https://doi.org/10.18637/jss.v067.i01.